Quasiperiodic Poincaré persistence at high degeneracy
DOI10.1016/j.aim.2023.109399arXiv2111.11619MaRDI QIDQ6182776
Xue Yang, Yong Li, Weichao Qian
Publication date: 21 December 2023
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.11619
Hamiltonian systemsKAM theoryresonant invariant torihigh-order degenerate perturbationquasiperiodic Poincaré theorem
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) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Nearly integrable Hamiltonian systems, KAM theory (70H08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems
- Resonant tori of arbitrary codimension for quasi-periodically forced systems
- Invariant tori in Hamiltonian systems with high order proper degeneracy
- Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian
- On elliptic lower dimensional tori in Hamiltonian systems
- Perturbations of lower dimensional tori for Hamiltonian systems
- The surviving of lower dimensional tori from a resonant torus of Hamiltonian systems
- Nearly integrable infinite-dimensional Hamiltonian systems
- On Melnikov's persistency problem
- A quasi-periodic Poincaré's theorem
- KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems
- Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems
- Persistence of invariant tori on submanifolds in Hamiltonian systems
- Multiscale KAM theorem for Hamiltonian systems
- Melnikov's conditions in matrices
- Persistence of Lagrange invariant tori at tangent degeneracy
- Regular and singular reductions in the spatial three-body problem
- Asymptotic density of collision orbits in the restricted circular planar 3 body problem
- Convergent series expansions for quasi-periodic motions
- Periodic Solutions and KAM Tori in a Triaxial Potential
- Persistence of lower dimensional tori of general types in Hamiltonian systems
- Degenerate lower-dimensional tori under the Bryuno condition
- Morse Theory. (AM-51)
- Differential Topology
- Density of convex billiards with rational caustics
- Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori
- Partial preservation of frequencies in KAM theory
- THE ISOENERGETIC KAM-TYPE THEOREM AT RESONANT CASE fOR NEARLY INTEGRABLE HAMILTONIAN SYSTEMS
