On the persistence of degenerate lower-dimensional tori in reversible systems
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Publication:3192329
DOI10.1017/etds.2014.34zbMath1351.37231OpenAlexW2075785243MaRDI QIDQ3192329
Xiaocai Wang, Junxiang Xu, Dongfeng Zhang
Publication date: 12 October 2015
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/etds.2014.34
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Cites Work
- Unnamed Item
- Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems
- On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point
- 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
- A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
- Unfoldings of quasi-periodic tori in reversible systems
- On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems
- Quasi-periodic bifurcations in reversible systems
- Degenerate lower-dimensional tori in Hamiltonian systems
- Convergent series expansions for quasi-periodic motions
- Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation
- Persistence of lower dimensional tori of general types in Hamiltonian systems
- Integrability of hamiltonian systems on cantor sets
- 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
- 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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