双曲混沌

《双曲混沌:一个物理学家的观点(英文版)》为非线性物理科学之一。

本书从物理学而不是数学概念的角度介绍了动力系统中均匀双曲吸引子目前的进展。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，本书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。 本书可以作为本科高年级和研究生教材，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专著。 关键词：动力系统、混沌、奇怪吸引子, Plykin 吸引子, Smale – Williams  吸引子, 双曲吸引子

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

Part1BasicNotionsandReview
DynamicalSystemsandHyperbolicity
1.1Dynamicalsystems:basicnotions
1.1.1Systemswithcontinuousanddiscretetime,andtheirmutualrelation
1.1.2Dynamicsintermsofphasefluid:Conservativeanddissipativesystemsandattractors
1.1.3Roughsystemsandstructuralstability
1.1.4Lyapunovexponentsandtheircomputation
1.2Modelexamplesofchaoticattractors
1.2.1Chaosintermsofphasefluidandbaker'smap
1.2.2Smale-Williamssolenoid
1.2.3DA-attractor
1.2.4Plykintypeattractors
1.3Notionofhyperbolicity
1.4Contentandconclusionsofthehyperbolictheory
1.4.1Conecriterion.
1.4.2Instability
1.4.3TransversalCantorstructureandKaplan-Yorkedimension
1.4.4Markovpartitionandsymbolicdynamics
1.4.5Enumeratingoforbitsandtopologicalentropy
1.4.6Structuralstability
1.4.7InvariantmeasureofSinai-Ruelle-Bowen
1.4.8Shadowingandeffectofnoise
1.4.9Ergodicityandmixing
1.4.10Kolmogorov-Sinaientropy
References
2PossibleOccurrenceofHyperbolicAttractors
2.1TheNewhouse-Ruelle-Takenstheoremanditsrelationtotheuniformlyhyperbolicattractors
2.2Lorenzmodelanditsmodifications
2.3Somemapswithuniformlyhyperbolicattractors
2.4FromDAtothePlykintypeattractor
2.5Hunt'sexample:SuspendingthePlykintypeattractor
2.6Thetriplelinkage:Amechanicalsystemwithhyperbolicdynamics
2.7ApossibleoccurrenceofaPlykintypeattractorinHindmarsh-Roseneuronmodel
2.8BlueskycatastropheandbirthoftheSmale-Williamsattractor
2.9Taffy-pullingmachine
References

Part2Low-DimensionalModels
KickedMechanicalModelsandDifferentialEquationswithPeriodicSwitch
3.1Smale-Williamssolenoidinmechanicalmodel:Motionofaparticleonaplaneunderperiodickicks
3.2AsetofswitchingdifferentialequationswithattractorofSmale-Williamstype
3.3ExplicitdynamicalsystemwithattractorofPlykintype
3.3.1Plykintypeattractoronasphere
3.3.2Plykintypeattractorontheplane
3.4Plykin-likeattractorinsmoothnon-autonomoussystem
References
Non-AutonomousSystemsofCoupledSerf-Oscillators
4.1VanderPoloscillator
4.2Smale-Williamsattractorinanon-autonomoussystemofalternatelyexcitedvanderPoloscillators
4.3SystemofalternatelyexcitedvanderPoloscillatorsintermsofslowcomplexamplitudes
4.4Non-resonanceexcitationtransfer
4.5Plykin-likeattractorinnon-autonomouscoupledoscillators
4.5.1Representationofstatesonasphereandequationsofthemodel
4.5.2Numericalresultsforthecoupledoscillators
References
5AutonomousLow-dimensionalSystemswithUniformlyHyperbolic
AttractorsinthePoincar~Maps
5.1Autonomoussystemoftwocoupledoscillatorswithself-regulatingalternatingexcitation
……
Part3Higher-DimensionalSystemsandPhenomena
Part4ExperimentalStudies