6533b86ffe1ef96bd12cea02

RESEARCH PRODUCT

Integrability via Reversibility

Maciej P. Wojtkowski

subject

Pure mathematicsClass (set theory)Dense setGeneral Physics and AstronomyLyapunov exponentDynamical Systems (math.DS)IntegrabilityCoexistence of integrability and chaotic behavior01 natural sciencessymbols.namesakeReversibility0103 physical sciencesFOS: MathematicsOrder (group theory)0101 mathematicsInvariant (mathematics)Mathematics - Dynamical SystemsMathematical PhysicsMathematicsComplement (set theory)010102 general mathematicsTorusPhase spacesymbols010307 mathematical physicsGeometry and Topology

description

Abstract A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying quasi-periodic motions, and this behavior persists under perturbations within the class. Real-analytic volume preserving systems are found in this class which have positive Lyapunov exponents on an open subset, and the complement filled with invariant tori.

yearjournalcountryeditionlanguage
2017-05-01
http://arxiv.org/abs/1502.03074