Normally Hyperbolic Invariant Cylinders Passing Through Multiple Resonance

2020/01/30 by Chong-Qing Cheng, Min Zhou, Cheng, Chong-Qing +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2001.11223

openalex publication_date 2020/01/30 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28

Abstract

We study the continuation of periodic orbits from various compound of homoclinics in classical system. Together with the homoclinics, the periodic orbits make up a C¹-smooth, normally hyperbolic invariant cylinder with holes. It plays a key role to cross multiple resonant point.

Citations

• Action minimizing invariant measures for positive definite Lagrangian systems

Related

• Uniform hyperbolicity of invariant cylinder
• Normally hyperbolic invariant manifolds near strong double resonance
• A way to cross double resonance
• Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions
• Resonances associated to a closed hyperbolic trajectory in dimension 2