Mixed dynamics in a parabolic standard map

DOI10.1016/j.physd.2015.09.003zbMath1364.37092arXiv1504.01197OpenAlexW1786392513MaRDI QIDQ2357460

Lev M. Lerman, James D. Meiss

Publication date: 13 June 2017

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01197

zbMATH Keywords

non-uniform hyperbolicityelliptic periodic orbits

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Simulation of dynamical systems (37M05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items

Regimes of stability of accelerator modes, Differentiable invariant manifolds of nilpotent parabolic points, Invariant manifolds of parabolic fixed points. I: Existence and dependence on parameters

Cites Work

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• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Breaking hyperbolicity for smooth symplectic toral diffeomorphisms
• On stochastic sea of the standard map
• Chaotic trajectories in the standard map. The concept of anti- integrability
• Time-reversal symmetry in dynamical systems: a survey
• Transport in Hamiltonian systems
• Resonances in area-preserving maps
• Lyapunov functions and topological stability
• Bernoulli diffeomorphisms on surfaces
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• SRB measures of certain almost hyperbolic diffeomorphisms with a tangency
• Locally compact groups of differentiable transformations
• Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour
• Elliptic isles in families of area-preserving maps
• Symplectic maps, variational principles, and transport
• Smooth models of Thurston's pseudo-Anosov maps
• Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
• Stable curves asymptotic to a degenerate fixed point
• Genericity of zero Lyapunov exponents
• Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• The Poincare-Bendixson Theorem for the Klein Bottle
• Differentiable dynamical systems
• Invariant manifolds