以上两个答案有冲突呢，话说詹姆斯。格莱克著有《混沌学》一书，最早是谁引进中国没人清楚，似乎没人对这理论感兴趣，你是从哪里接触的呢？ 就现在来说，似乎只有刘慈欣的《混沌蝴蝶》里提到过
混沌在数学分析上表现为迭代数列在初始值不同时其收敛性的不同,以及对不动点和周期的研究,可参阅谢惠民等编的<数学分析习题课讲义>中6和6两节。
首字母不同,这你都看不出来，其实没什么
1972年12月29日，美国麻省理工学院教授、混沌学开创人之一EN洛伦兹在美国科学发展学会第139次会议上发表了题为《蝴蝶效应》的论文~从而提出了混沌学理论~ 有关引进中国的问题~ 《礼记·经解》：“《易》曰：‘君子慎始，差若毫厘，缪以千里。’”《魏书·乐志》：“但气有盈虚，黍有巨细，差之毫厘，失之千里。”可见中国在1300年前就已经对于混沌学有相应记载了~所以这个引进人物~不太好说~
您好，请问您的论文是什么方向呢？1）一般数学专业类SCI杂志论文数量都200篇以下（当然化学、生物等超过1000篇的多的是，所以学化学生物医学等人员发表SCI数量特多屡见不鲜），高数量的专业SCI杂志都很好发，如下：2008年论文数量 2010年中科院大类分区Journal of Mathematical Analysis and Applications 1220 2区Applied Mathematics and Computation 1088 2区2009年论文数量Nonlinear Analysis: Theory, Methods & Applications 1007 2区Chaos, Solitons and Fractals 1278 2区（物理）2010年论文数量Journal of Computational and Applied Mathematics 586 2区Computers and Mathematics with Applications 695 3区（划工程类）Nonlinear Analysis: Real World Applications 421 1区Communications in Nonlinear Science and Numerical Simulation 407 2区 (划物理类）International journal of nonlinear sciences and numerical simulation 1区（划工程类）国内许多学者在同一个期刊上一年发表论文超过10篇的大陆学者多的是。浙江大学很英明，最近，学校列了个800多种认可的权威（或名牌）期刊（不看影响因子和分区），把这些期刊全部踢出去了。浙江大学发展如此之快，决策英明呀！投稿学者需慎重！（2）有胸怀大志者，推荐发表如下期刊：（大陆学者在几个知名的数学期刊发表论文十分困难,数量极少Annals of Mathematics2000-2005年,1篇，南开大学M A M S 2000-2005年,无B A M S 000-2005年,3篇，北大2篇，J A M S 2000-2005年,1篇，香港科技大学1篇IM2000-2005年,6篇，中科院1篇，香港大学1篇，南开1篇，川大2篇，中山1篇
GoingPub 最新SCI期刊查询及分析系统（2018-2019年）整理了最新SCI收录的详细信息，分属领域，研究方向，中科院SCI期刊分区等。可在这查 /journal/
将所有SCI期刊按影响因子排序，前5%是一区，前20%是二区一般SCI论文分四个区，一区都是国际顶级期刊，二区次之，
你好，关于SCI分区，主要有两个，一个是中科院分区，一个是汤森路透分区，他们都有四个区，你是的一区和二区，我分别给你说一下你就明白了。中科院分区：前5%为该类的1区，6%-20%为2区，21%-50%为3区，其余的为4区，该分区1-4区呈金字塔状分布，越往上杂志质量越高；汤森路透分区（简称ICR）：前25%（含25%）为Q1区，前25%-50%（含50%）为Q2区，前50%-75%（含75%）为Q3区，75%之后为Q4区，JCR的每个学科分类按照期刊的影响因子高低，平均分为Q1、Q2、Q3、和Q4这四个区的。拓展资料：中科院分区和JCR分区图中科院分区汤森路透（JCR）分区图片来源：百度
chaos 英音：['kei�0�0s]美音：['keɑs] 混沌 发表在美国物理协会The American Institute of Physics的杂志《混沌》Chaos上的一项 混乱chaos 混乱吵闹可以记做吵死的汉语拼音加记忆 quaint 古怪的怪的汉语拼音guai把q用g 紊乱427 chaos n 混乱紊乱 428 discount n价格折扣 429 display nvt 陈列展览 Chaos 混乱度 Chaos混乱混乱度 Character角色 Character Structures角色结构 Child孩子 浑沌怪 72 Chaos 浑沌怪 73 Dark Awakening 五面怪的诡计 74 Forever Is a Long Time Coming
您好，请问您的论文是什么方向呢？1）一般数学专业类SCI杂志论文数量都200篇以下（当然化学、生物等超过1000篇的多的是，所以学化学生物医学等人员发表SCI数量特多屡见不鲜），高数量的专业SCI杂志都很好发，如下：2008年论文数量 2010年中科院大类分区Journal of Mathematical Analysis and Applications 1220 2区Applied Mathematics and Computation 1088 2区2009年论文数量Nonlinear Analysis: Theory, Methods & Applications 1007 2区Chaos, Solitons and Fractals 1278 2区（物理）2010年论文数量Journal of Computational and Applied Mathematics 586 2区Computers and Mathematics with Applications 695 3区（划工程类）Nonlinear Analysis: Real World Applications 421 1区Communications in Nonlinear Science and Numerical Simulation 407 2区 (划物理类）International journal of nonlinear sciences and numerical simulation 1区（划工程类）国内许多学者在同一个期刊上一年发表论文超过10篇的大陆学者多的是。浙江大学很英明，最近，学校列了个800多种认可的权威（或名牌）期刊（不看影响因子和分区），把这些期刊全部踢出去了。浙江大学发展如此之快，决策英明呀！投稿学者需慎重！（2）有胸怀大志者，推荐发表如下期刊：（大陆学者在几个知名的数学期刊发表论文十分困难,数量极少Annals of Mathematics2000-2005年,1篇，南开大学M A M S 2000-2005年,无B A M S 000-2005年,3篇，北大2篇，J A M S 2000-2005年,1篇，香港科技大学1篇IM2000-2005年,6篇，中科院1篇，香港大学1篇，南开1篇，川大2篇，中山1篇
您好，请问您的论文是什么方向呢？1）一般数学专业类SCI杂志论文数量都200篇以下（当然化学、生物等超过1000篇的多的是，所以学化学生物医学等人员发表SCI数量特多屡见不鲜），高数量的专业SCI杂志都很好发，如下：2008年论文数量 2010年中科院大类分区Journal of Mathematical Analysis and Applications 1220 2区Applied Mathematics and Computation 1088 2区2009年论文数量Nonlinear Analysis: Theory, Methods & Applications 1007 2区Chaos, Solitons and Fractals 1278 2区（物理）2010年论文数量Journal of Computational and Applied Mathematics 586 2区Computers and Mathematics with Applications 695 3区（划工程类）Nonlinear Analysis: Real World Applications 421 1区Communications in Nonlinear Science and Numerical Simulation 407 2区 (划物理类）International journal of nonlinear sciences and numerical simulation 1区（划工程类）国内许多学者在同一个期刊上一年发表论文超过10篇的大陆学者多的是。浙江大学很英明，最近，学校列了个800多种认可的权威（或名牌）期刊（不看影响因子和分区），把这些期刊全部踢出去了。浙江大学发展如此之快，决策英明呀！投稿学者需慎重！（2）有胸怀大志者，推荐发表如下期刊：（大陆学者在几个知名的数学期刊发表论文十分困难,数量极少Annals of Mathematics2000-2005年,1篇，南开大学M A M S 2000-2005年,无B A M S 000-2005年,3篇，北大2篇，J A M S 2000-2005年,1篇，香港科技大学1篇IM2000-2005年,6篇，中科院1篇，香港大学1篇，南开1篇，川大2篇，中山1篇
这几个题目每一个都有很多内容可以挖掘，而且网上的论文多的数不清，建议你到sci上查查，会有很多的，但是pdf格式的，我没法考给你。但是如果你要是为了对付老师混毕业，对不起，没法帮你。
混沌学 Chaos theoryIn mathematics, chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect) As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements This behavior is known as deterministic chaos, or simply Chaotic behaviour is also observed in natural systems, such as the This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural OverviewChaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical Observations of chaotic behaviour in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular Everyday examples of chaotic systems include weather and [1] There is some controversy over the existence of chaotic dynamics in the plate tectonics and in [2][3][4]Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete A related field of physics called quantum chaos theory studies systems that follow the laws of quantum Recently, another field, called relativistic chaos,[5] has emerged to describe systems that follow the laws of general As well as being orderly in the sense of being deterministic, chaotic systems usually have well defined [citation needed] For example, the Lorenz system pictured is chaotic, but has a clearly defined Bounded chaos is a useful term for describing models of HistoryThe first discoverer of chaos was Henri Poincaré In 1890, while studying the three-body problem, he found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed [6] In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative [7] In the system studied, "Hadamard's billiards," Hadamard was able to show that all trajectories are unstable in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov Much of the earlier theory was developed almost entirely by mathematicians, under the name of ergodic Later studies, also on the topic of nonlinear differential equations, were carried out by GD Birkhoff,[8] A N Kolmogorov,[9][10][11] ML Cartwright and JE Littlewood,[12] and Stephen S[13] Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and L Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behaviour of certain experiments like that of the logistic What had been beforehand excluded as measure imprecision and simple "noise" was considered by chaos theories as a full component of the studied The main catalyst for the development of chaos theory was the electronic Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these One of the earliest electronic digital computers, ENIAC, was used to run simple weather forecasting An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in [14] Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather He wanted to see a sequence of data again and to save time he started the simulation in the middle of its He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last To his surprise the weather that the machine began to predict was completely different from the weather calculated Lorenz tracked this down to the computer The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 506127 was printed as This difference is tiny and the consensus at the time would have been that it should have had practically no However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term [15] Lorenz's discovery, which gave its name to Lorenz attractors, proved that meteorology could not reasonably predict weather beyond a weekly period (at most)The year before, Benoit Mandelbrot found recurring patterns at every scale in data on cotton [16] Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating [17] Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, , in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards)[18][19] In 1967, he published "How long is the coast of Britain? Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring [20] Arguing that a ball of twine appears to be a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 2619, the Menger sponge and the Sierpiński gasket) In 1975 Mandelbrot published The Fractal Geometry of Nature, which became a classic of chaos Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal Chaos was observed by a number of experimenters before it was recognized; , in 1927 by van der Pol[21] and in 1958 by RL I[22][23] However, Yoshisuke Ueda seems to have been the first experimenter to have identified a chaotic phenomenon as such by using an analog computer on November 27, The chaos exhibited by an analog computer is a real phenomenon, in contrast with those that digital computers calculate, which has a different kind of limit on Ueda's supervising professor, Hayashi, did not believe in chaos, and thus he prohibited Ueda from publishing his findings until [24]In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz), and the meteorologist Edward LThe following year, Mitchell Feigenbaum published the noted article "Quantitative Universality for a Class of Nonlinear Transformations", where he described logistic [25] Feigenbaum had applied fractal geometry to the study of natural forms such as Feigenbaum notably discovered the universality in chaos, permitting an application of chaos theory to many different In 1979, Albert J Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in convective Rayleigh–Benard He was awarded the Wolf Prize in Physics in 1986 along with Mitchell J Feigenbaum "for his brilliant experimental demonstration of the transition to turbulence and chaos in dynamical systems"[26]The New York Academy of Sciences then co-organized, in 1986, with the National Institute of Mental Health and the Office of Naval Research the first important conference on Chaos in biology and Bernardo Huberman thereby presented a mathematical model of the eye tracking disorder among [27] Chaos theory thereafter renewed physiology in the 1980s, for example in the study of pathological cardiac In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in Physical Review Letters[28] describing for the first time self-organized criticality (SOC), considered to be one of the mechanisms by which complexity arises in Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have centred around large-scale natural or social systems that are known (or suspected) to display scale-invariant Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[29] describing the frequency of aftershocks); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould) Worryingly, given the implications of a scale-free distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of These "applied" investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling The same year, James Gleick published Chaos: Making a New Science, which became a best-seller and introduced general principles of chaos theory as well as its history to the broad At first the domains of work of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems Alluding to Thomas Kuhn's concept of a paradigm shift exposed in The Structure of Scientific Revolutions (1962), many "chaologists" (as some self-nominated themselves) claimed that this new theory was an example of such as shift, a thesis upheld by J GThe availability of cheaper, more powerful computers broadens the applicability of chaos Currently, chaos theory continues to be a very active area of research, involving many different disciplines (mathematics, topology, physics, population biology, biology, meteorology, astrophysics, information theory, )[edit] Chaotic dynamicsFor a dynamical system to be classified as chaotic, it must have the following properties:[30]it must be sensitive to initial conditions, it must be topologically mixing, and its periodic orbits must be Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future Sensitivity to initial conditions is popularly known as the "butterfly effect", so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, DC entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale Had the butterfly not flapped its wings, the trajectory of the system might have been vastly Sensitivity to initial conditions is often confused with chaos in popular It can also be a subtle property, since it depends on a choice of metric, or the notion of distance in the phase space of the For example, consider the simple dynamical system produced by repeatedly doubling an initial value (defined by iterating the mapping on the real line that maps x to 2x) This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points will eventually become widely However, it has extremely simple behaviour, as all points except 0 tend to If instead we use the bounded metric on the line obtained by adding the point at infinity and viewing the result as a circle, the system no longer is sensitive to initial For this reason, in defining chaos, attention is normally restricted to systems with bounded metrics, or closed, bounded invariant subsets of unbounded Even for bounded systems, sensitivity to initial conditions is not identical with For example, consider the two-dimensional torus described by a pair of angles (x,y), each ranging between zero and 2π Define a mapping that takes any point (x,y) to (2x, y + a), where a is any number such that a/2π is Because of the doubling in the first coordinate, the mapping exhibits sensitive dependence on initial However, because of the irrational rotation in the second coordinate, there are no periodic orbits, and hence the mapping is not chaotic according to the definition Topologically mixing means that the system will evolve over time so that any given region or open set of its phase space will eventually overlap with any other given Here, "mixing" is really meant to correspond to the standard intuition: the mixing of colored dyes or fluids is an example of a chaotic Linear systems are never chaotic; for a dynamical system to display chaotic behaviour it has to be Also, by the Poincaré–Bendixson theorem, a continuous dynamical system on the plane cannot be chaotic; among continuous systems only those whose phase space is non-planar (having dimension at least three, or with a non-Euclidean geometry) can exhibit chaotic However, a discrete dynamical system (such as the logistic map) can exhibit chaotic behaviour in a one-dimensional or two-dimensional phase [edit] AttractorsSome dynamical systems are chaotic everywhere (see Anosov diffeomorphisms) but in many cases chaotic behaviour is found only in a subset of phase The cases of most interest arise when the chaotic behaviour takes place on an attractor, since then a large set of initial conditions will lead to orbits that converge to this chaotic An easy way to visualize a chaotic attractor is to start with a point in the basin of attraction of the attractor, and then simply plot its subsequent Because of the topological transitivity condition, this is likely to produce a picture of the entire final For instance, in a system describing a pendulum, the phase space might be two-dimensional, consisting of information about position and One might plot the position of a pendulum against its A pendulum at rest will be plotted as a point, and one in periodic motion will be plotted as a simple closed When such a plot forms a closed curve, the curve is called an Our pendulum has an infinite number of such orbits, forming a pencil of nested ellipses about the [edit] Strange attractorsWhile most of the motion types mentioned above give rise to very simple attractors, such as points and circle-like curves called limit cycles, chaotic motion gives rise to what are known as strange attractors, attractors that can have great detail and For instance, a simple three-dimensional model of the Lorenz weather system gives rise to the famous Lorenz The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because not only was it one of the first, but it is one of the most complex and as such gives rise to a very interesting pattern which looks like the wings of a Another such attractor is the Rössler map, which experiences period-two doubling route to chaos, like the logistic Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map) Other discrete dynamical systems have a repelling structure called a Julia set which forms at the boundary between basins of attraction of fixed points - Julia sets can be thought of as strange Both strange attractors and Julia sets typically have a fractal The Poincaré-Bendixson theorem shows that a strange attractor can only arise in a continuous dynamical system if it has three or more However, no such restriction applies to discrete systems, which can exhibit strange attractors in two or even one dimensional The initial conditions of three or more bodies interacting through gravitational attraction (see the n-body problem) can be arranged to produce chaotic Minimum complexity of a chaotic systemSimple systems can also produce chaos without relying on differential An example is the logistic map, which is a difference equation (recurrence relation) that describes population growth over Another example is the Ricker model of population Even the evolution of simple discrete systems, such as cellular automata, can heavily depend on initial Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule A minimal model for conservative (reversible) chaotic behavior is provided by Arnold's cat
混沌在数学分析上表现为迭代数列在初始值不同时其收敛性的不同,以及对不动点和周期的研究,可参阅谢惠民等编的<数学分析习题课讲义>中6和6两节。
Noether's theorem 很恶心阿，关键大家都明白还要硬严密推导。如果你擅长用微小量计算，建议选这个，然后导出微小平移和旋转的向量表达式。个人觉得可以把the works of Lagrange 和the works of Hamilton 结合起来解释某些具体问题。这里works不是著作是功，也就是著名的Lagrange 和 Hamilton 最典型的就是单摆了，dp/dt=-dH/dq,dq/dt=dH/[p,q]=可以从不同的角度解析，并给出p-qGraph,就是那个一圈一圈的，按E的不同分3种情况讨论运动。最后在深入，如果角度不可近似，那么就要用到chaos理论的分歧方程式，其实就是椭圆函数拉。应该可以把内容融会起来。