Arnold diffusion for cusp-generic nearly integrable convex systems on \mathbb A³

2016/02/07 by Juan Pablo Araya Marco, Marco, Jean-Pierre
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1602.02403

openalex publication_date 2016/02/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove the existence of "Arnold diffusion orbits" in cusp-generic nearly integrable a priori stable systems on \mathbb A³. The result relies on the cusp-generic existence of chains in nearly integrable a priori stable systems, proved in a previous paper, together with the existence of diffusion orbits along such chains. The latter result was obtained in collaboration with M. Gidea.

Related

• Chains of compact cylinders for cusp-generic nearly integrable convex systems on \mathbbA³
• Arnold diffusion in nearly integrable Hamiltonian systems
• Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom
• Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders
• Arnold diffusion in multidimensional a priori unstable Hamiltonian systems