Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps

DOI10.1137/22M1485103OpenAlexW4221160751MaRDI QIDQ5887854

Xiaolong He, Rafael de la Llave

Publication date: 14 April 2023

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.09146

zbMATH Keywords

resonancephase lockingLindstedt seriesKAMfoliation preserving torus mapSternberg linearizationtime reparameterization of irrational flows

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10)

Related Items (2)

Simultaneous conjugation of commuting foliation preserving torus maps ⋮ Quasi-periodic solutions for differential equations with an elliptic equilibrium under delayed perturbation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Resonant equilibrium configurations in quasi-periodic media: perturbative expansions
• Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case.
• Resonance regions for Mathieu type dynamical systems on a torus
• Frequency modulation indicator, Arnold's web and diffusion in the Stark-quadratic-Zeeman problem
• Invariant manifolds associated to nonresonant spectral subspaces
• Phase-locking for dynamical systems on the torus and perturbation theory for Mathieu-type problems
• Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall
• Regularity of the composition operator in spaces of Hölder functions
• Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case
• Convergent series expansions for quasi-periodic motions
• Resonant Equilibrium Configurations in Quasi-Periodic Media: KAM Theory
• A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
• Geography of resonances and Arnold diffusion ina prioriunstable Hamiltonian systems
• Resonance regions for families of torus maps
• Weak mixing for reparameterized linear flows on the torus
• KAM Theory for Quasi-periodic Equilibria in One-Dimensional Quasi-periodic Media
• Classical Fourier Analysis

This page was built for publication: Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps