本书从物理学而不是数学概念的角度介绍了目前动力系统中均匀双曲吸引子研究的进展小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。
Part I Basic Notions and Review
Part II Low-Dimensional Models
Part III Higher-Dimensional Systems and Phenomena
Part IV Experimental Studies
Appendix AComputation of Lyapunov Exponents:The BenettinAlgorithm
Appendix BHenon and Ikeda Maps
References
Appendix C Smales Horseshoe and Homoclinic Tangle
References
Appendix DFractal Dimensions and Kaplan-Yorke Formula
References
Appendix EHunts Model: Formal Definition
References
Appendix FGeodesics on a Compact Surface of NegativeCurvature
ReferencesPart I Basic Notions and Review
Part II Low-Dimensional Models
Part III Higher-Dimensional Systems and Phenomena
Part IV Experimental Studies
Appendix AComputation of Lyapunov Exponents:The BenettinAlgorithm
Appendix BHenon and Ikeda Maps
References
Appendix C Smales Horseshoe and Homoclinic Tangle
References
Appendix DFractal Dimensions and Kaplan-Yorke Formula
References
Appendix EHunts Model: Formal Definition
References
Appendix FGeodesics on a Compact Surface of NegativeCurvature
References
Appendix G Effect of Noise in a System with a HyperbolicAttractor
References
Index
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。