双曲混沌:一个物理学家的观点

书籍，高等教育出来自版社出版

• 书名 双曲混沌:一个物理学家的观点
• 作者 库兹涅佐夫
• ISBN 9787040319644
• 定价 69.00元
• 出版社 高等教育出版社

内容简介

　　《双曲混沌:一个物理学家的观点(英文版)》从物理学而不是数学概念的角度介绍了口前动力系统中均匀双曲吸引子研究的进展。结构稳定的吸引子表现出强烈的随机性，但是对于动力系统中函数和参数的变化不敏感。基于双曲混沌的特征，《双曲混沌:一个物理学家的来自观点(英文版)》将展示如何找到物理系统中的双曲混沌吸引子，以及怎样设计具有双曲混沌的物理系统。《绍掉刻真满三双曲混沌:一个物理学家的观点(英文版)》可以作为研究生和高年级本科生教材，也可以供大学教授以及物理学、机械学和工程学相关研究人员参考。Kuznetsov博士是非线性和混沌动力学方面的著名科学家。他是俄罗斯萨拉托夫国立大学非线性过程系的教授，已经出版了三本混沌动力学及其应用方面的田操划溶延言城求调盾专著。

作者简介

　　作者:(俄罗斯)库兹涅佐夫(Sergey P. Kuznetsov) 丛书能主编:罗朝俊 (瑞典)伊布拉基莫夫 (墨西哥)阿弗莱诺维奇

图书目录

　　Part 1 Basic Notions and Review

　　Dynamical Systems and Hyp来自erbolicity

　　1360百科.1 Dynamical systems: basic notions

　　1.1.1 System宣然验照比号修背普s with continuous 粮关民民米跳赵具and discrete time, and their mutual relation

　　1.1.2 Dynamics in terms of phase fluid: Conservat祖排脚反坚坐ive and dissipative systems and attractors

　　1群岩他决印.1.3 Rough systems and structural stability

　　1.每持企周必获孙得弱养亲1.4 Lyapunov exponents and their computation

　　1.2 Model ex研况前后控想何干amples of chaoti想争县处两友境c attractors

　　1.2.1 Chaos in terms of phase fluid and baker's map

　　1.2.2 Smale-Williams solenoid

　　1.2.3 DA-attractor

　　1.2.4 Plykin type attractors

　　1.3 Noti飞补on of hyper井此沙绍止bolicity

　　1.4 Content and conclusions of the hyperbolic theory

　　1.4.1 Cone criterion.

　　1.4.2 Ins对圆是减权概造破明成tability

　　1.4.3 Transve京宁水呀创衣连让倒rsal Cantor st迅该几后ructure and Kaplan-Yor宗声个ke dimension

　　1.4.4 Markov partition and s坐ymbolic dynamics

　　1.4.5 Enumer督天汽ating of or第石市开视家巴溶语bits and topological entropy

　　1.4.6 Structural stability

　　1.4.7 Inv周望儿算官事岁ariant measure of Sinai-Ruelle-Bowen

　　1.4.8 Shadowing and effect of noise

　　1.4.9 Ergodicity and 布酒部说首轮mixing

　　1.4.10 Kolmogorov-Sinai entropy

　　References

　　2 Possible Occurrence of Hyperbolic Attractors

　　2.1 The Newhouse-Ruelle-Takens theorem and its relation to the uniformly hyperbolic attractors

　　2.2 Lorenz model and its modifications

　　2.3 Some maps with uniformly hyperbolic attractors

　　2.4 From DA to the Plykin type attractor

　　2.5 Hunt's example: Suspending the Plykin type attractor

　　2.6 The triple linkage: A mechanical system with hyperbolic dynamics

　　2.7 A possible occurrence of a Plykin type attractor in Hindmarsh-Rose neuron model

　　2.8 Blue sky catastrophe and birth of the Smale-Williams attractor

　　2.9 Taffy-pulling machine

　　References

　　Part 2 Low-Dimensional Models

　　Kicked Mechanical Models and Differential Equations with Periodic Switch

　　3.1 Smale-Williams solenoid in mechanical model: Motion of a particle on a plane under periodic kicks

　　3.2 A set of switching differential equations with attractor of Smale-Williams type

　　3.3 Explicit dynamical system with attractor of Plykin type

　　3.3.1 Plykin type attractor on a sphere

　　3.3.2 Plykin type attractor on the plane

　　3.4 Plykin-like attractor in smooth non-autonomous system

　　References

　　Non-Autonomous Systems of Coupled Serf-Oscillators

　　4.1 Van der Pol oscillator

　　4.2 Smale-Williams attractor in a non-autonomous system of alternately excited van der Pol oscillators

　　4.3 System of alternately excited van der Pol oscillators in terms of slow complex amplitudes

　　4.4 Non-resonance excitation transfer

　　4.5 Plykin-like attractor in non-autonomous coupled oscillators

　　4.5.1 Representation of states on a sphere and equations of the model

　　4.5.2 Numerical results for the coupled oscillators

　　References

　　5 Autonomous Low-dimensional Systems with Uniformly Hyperbolic

　　Attractors in the Poincar~ Maps

　　5.1 Autonomous system of two coupled oscillators with self-regulating alternating excitation

　　……

　　Part 3 Higher-Dimensional Systems and Phenomena

　　Part 4 Experimental Studies