Geometric and statistical properties induced by separatrix crossings in volume-preserving systems

DOI10.1088/0951-7715/16/2/310zbMath1038.37017OpenAlexW1977693002MaRDI QIDQ4415733

Carles Simó, Aleksey A. Vasiliev, Anatoly I. Neishtadt

Publication date: 6 August 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/16/2/310

zbMATH Keywords

chaotic motionadiabatic invariantseparatrixvolume-preserving systemaveraged system

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (7)

Integrability analysis of the stretch-twist-fold flow ⋮ Jump of the adiabatic invariant at a separatrix crossing: degenerate cases ⋮ On passage through resonances in volume-preserving systems ⋮ Some remarks on the abundance of stable periodic orbits inside homoclinic lobes ⋮ Nonintegrability of dynamical systems with homo- and heteroclinic orbits ⋮ Mixing properties of steady flow in thermocapillary driven droplets ⋮ Resonance phenomena and long-term chaotic advection in volume-preserving systems

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