Hyperbolicity, transversality and analytic first integrals.

DOI10.1016/J.JDE.2003.10.002zbMath1034.37018OpenAlexW1973494922MaRDI QIDQ1428256

Jacky Cresson

Publication date: 14 March 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.10.002

zbMATH Keywords

Three-body problemAnalytic first integralNormally hyperbolic manifoldPartially hyperbolic tori

Mathematics Subject Classification ID

Three-body problems (70F07) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Invariant manifold theory for dynamical systems (37D10)

Related Items (1)

Analytic integrability of a Chua system

Cites Work

• Unnamed Item
• Global bifurcations and chaos. Analytical methods
• Arnold diffusion and oscillatory solutions in the planar three-body problem
• Transversal intersection of separatrices and branching of solutions as obstructions to the existence of an analytic integral in many-dimensional systems. I: Basic result: Separatrices of hyperbolic periodic points
• Arnol'd diffusion in the elliptic restricted three-body problem
• Hyperbolicité et non-intégrabilité analytique. II. Tores normalement et partiellement hyperboliques
• Stable and Random Motions in Dynamical Systems
• THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS

This page was built for publication: Hyperbolicity, transversality and analytic first integrals.