Some remarks on the problem of ergodicity of the standard map

DOI10.1016/S0375-9601(00)00452-7zbMath1115.37330WikidataQ125585424 ScholiaQ125585424MaRDI QIDQ997685

V. F. Lazutkin, Antonio Giorgilli

Publication date: 7 August 2007

Published in: Physics Letters. A (Search for Journal in Brave)

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Foundations of equilibrium statistical mechanics (82B03)

Related Items (7)

On Herman's positive entropy conjecture ⋮ Correlations in area preserving maps: a Shannon entropy approach ⋮ NUMERICAL APPROXIMATION OF THE PERCENTAGE OF ORDER FOR ONE-DIMENSIONAL MAPS ⋮ Ergodicity, mixing, and recurrence in the three rotor problem ⋮ Isentropic perturbations of a chaotic domain ⋮ SOME REMARKS ON THE GEOMETRY OF THE STANDARD MAP ⋮ Global dynamics and diffusion in the rational standard map

Cites Work

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• Plenty of elliptic islands for the standard family of area preserving maps
• Stable and Random Motions in Dynamical Systems
• A criterion for the positivity of the Liapunov characteristic exponent
• Invariant families of cones and Lyapunov exponents
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Making fractals fat.

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