Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems

DOI10.1007/s00332-017-9410-5zbMath1407.37100OpenAlexW2752322294MaRDI QIDQ1703000

Lu Xu, Yingfei Yi, Yong Li

Publication date: 1 March 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-017-9410-5

zbMATH Keywords

resonant toriKAM theorylower-dimensional torihigh-order proper degeneracymulti-scale Hamiltonian systems

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (9)

A Moser theorem for multiscale mappings ⋮ KAM in generalized Hamiltonian systems with multi-scales ⋮ Quasiperiodic Poincaré persistence at high degeneracy ⋮ On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori ⋮ On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori ⋮ On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors ⋮ Multiscale KAM theorem for Hamiltonian systems ⋮ Lower dimension tori of general types in multi-scale Hamiltonian systems ⋮ Persistence of Lagrange invariant tori at tangent degeneracy

Cites Work

• On Jupiter and his Galilean satellites: librations of de Sitter's periodic motions
• Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems
• Invariant tori in Hamiltonian systems with high order proper degeneracy
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• A quasi-periodic Poincaré's theorem
• Persistence of invariant tori on submanifolds in Hamiltonian systems
• Regular and singular reductions in the spatial three-body problem
• Corrigendum for the paper ``Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• Persistence of lower dimensional tori of general types in Hamiltonian systems
• Scaling Hamiltonian Systems
• THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS
• Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori
• ON POINCARÉ - TRESHCHEV TORI IN HAMILTONIAN SYSTEMS
• N-Dimensional Elliptic Invariant Tori for the Planar (N+1)-Body Problem
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

This page was built for publication: Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems