On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations
DOI10.3934/dcdsb.2022004OpenAlexW4210496733MaRDI QIDQ2081933
Xiaofei Cao, Xiaocai Wang, Xu-Qing Liu
Publication date: 30 September 2022
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdsb.2022004
Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) 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
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- On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems
- A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems
- A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems
- 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
- Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition
- Normal linear stability of quasi-periodic tori
- Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
- Quasi-periodic stability of normally resonant tori
- Reversible systems
- On elliptic lower dimensional tori in Hamiltonian systems
- Unfoldings of quasi-periodic tori in reversible systems
- Non-Floquet invariant tori in reversible systems
- On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues
- Quasi-periodic response solutions in forced reversible systems with Liouvillean frequencies
- Quasi-periodic bifurcations in reversible systems
- Convergent series expansions for quasi-periodic motions
- On the persistence of degenerate lower-dimensional tori in reversible systems
- THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION
- The iteration-approximation decoupling in the reversible KAM theory
- 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
- Partial preservation of frequencies in KAM theory
- Perturbations of lower dimensional tori in the resonant zone for reversible systems
- On lower dimensional invariant tori in reversible systems
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