Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

被引：0
作者：
Renato Vitolo
Henk Broer
Carles Simó
机构：
[1] University of Exeter,College of Engineering, Mathematics and Physical Sciences
[2] Harrison Building,Johann Bernoulli Institute for Mathematics and Computer Science
[3] University of Groningen,Departament de Matemàtica Aplicada i Anàlisi
[4] Universitat de Barcelona,undefined
来源：
Regular and Chaotic Dynamics | 2011年 / 16卷
关键词：
bifurcations; invariant tori; resonances; KAM theory; 37M20; 37C55; 37G30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.
引用
收藏
页码：154 / 184
页数：30
相关论文
共 127 条
[21]  
Takens F.(2009)The Quasi-Periodic Reversible Hopf Bifurcation Phys. D 238 309-318
[22]  
Newhouse S.E.(2007)Quasi-Periodic Stability of Normally Resonant Tori Nonlinearity 20 417-460
[23]  
Palis J.(1998)The Quasi-Periodic Hamiltonian Hopf Bifurcation Nonlinearity 11 667-770
[24]  
Takens F.(2003)Towards Global Models Near Homoclinic Tangencies of Dissipative Diffeomorphisms Nonlinearity 16 1751-1791
[25]  
Braaksma B. L. J.(2011)Normal-Internal Resonances in Quasi-Periodically Forced Oscillators: A Conservative Approach Regul. Chaotic Dyn. 16 39-50
[26]  
Broer H.W.(2008)Dynamics and Geometry Near Resonant Bifurcations Nonlinearity 21 1547-1578
[27]  
Wagener F. O. O.(2000)Generic Hopf-Neĭmark-Sacker Bifurcations in Feed Forward Systems Celestial Mech. Dynam. Astronom. 76 35-54
[28]  
Wagener F. O. O.(2001)On the Vertical Families of Two-Dimensional Tori Near the Triangular Points of the Bicircular Problem Nonlinearity 14 943-976
[29]  
Chenciner A.(2010)Numerical Computation of the Normal Behaviour of Invariant Curves of Discrete Contin. Dyn. Syst. Ser. B 14 41-74
[30]  
Chenciner A.(2010)-Dimensional Maps Discrete Contin. Dyn. Syst. Ser. B 14 75-109
12345678910