Persistence of multiscale degenerate invariant tori for reversible systems with multiscale degenerate equilibrium points

DOI10.1134/s1560354722060090zbMath1515.70020MaRDI QIDQ6038861

Dongfeng Zhang, Ru Qu

Publication date: 3 May 2023

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

topological degree theoryreversible systemKAM iterationDiophantine conditionGevrey smoothnessHerman methoddegenerate lower-dimensional torusfrequency mapping

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Cites Work

• Persistence of lower dimensional hyperbolic tori for reversible system
• Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations
• Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems
• Persistence of lower dimensional tori for a class of nearly integrable reversible systems
• Degenerate lower dimensional tori in reversible systems
• A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies
• Smooth linearization of commuting circle diffeomorphisms
• Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition
• Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
• Rigidity results for quasiperiodic \(\mathrm{SL}(2, \mathbb R)\)-cocycles
• On elliptic lower dimensional tori in Hamiltonian systems
• Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
• Reducibility of three dimensional skew symmetric system with Liouvillean basic frequencies
• Elliptic-type degenerate invariant tori for quasi-periodically forced four-dimensional non-conservative systems
• On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues
• On the reducibility of two-dimensional quasi-periodic systems with Liouvillean basic frequencies and without non-degeneracy condition
• Parabolic invariant tori in quasi-periodically forced skew-product maps
• Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems
• On the persistence of degenerate lower-dimensional tori in reversible systems
• Herman’s last geometric theorem
• The iteration-approximation decoupling in the reversible KAM theory
• Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
• Normal Form of Reversible Systems and Persistence of Lower Dimensional Tori under Weaker Nonresonance Conditions
• Reducibility of a class of nonlinear quasi-periodic systems with Liouvillean basic frequencies
• Completely degenerate responsive tori in Hamiltonian systems
• Partial preservation of frequencies in KAM theory
• Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter
• On lower dimensional invariant tori in reversible systems