Search results for "Coexistence of integrability and chaotic behavior"

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Integrability via Reversibility

2017

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.

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
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