Complete orbits for twist maps on the plane: the case of small twist

DOI10.1017/S0143385710000520zbMath1276.37035MaRDI QIDQ3093793

Rafael Ortega, Markus Kunze

Publication date: 18 October 2011

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

small twisttwist mapscomplete orbits

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical aspects of twist maps (37E40)

Related Items (12)

Complete Orbits for Twist Maps with Exponential Generating Functions ⋮ Global dynamics of the breathing circle billiard ⋮ Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ Dynamics of the Fermi–Ulam model in an external gravitational field ⋮ The existence of Aubry-Mather sets for the Fermi-Ulam model ⋮ Twist Mappings with Non-Periodic Angles ⋮ Rotation numbers and bounded deviations for quasi-periodic monotone recurrence relations ⋮ Escaping orbits are rare in the quasi-periodic Fermi–Ulam ping-pong ⋮ Chaotic motion in the breathing circle billiard ⋮ Growth rates of orbits in non-periodic twist maps and a theorem by Neishtadt ⋮ Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials ⋮ On the global dynamical properties of a Fermi–Ulam model

Cites Work

• Complete orbits for twist maps on the plane
• Invariant curves and time-dependent potentials
• Instability in Fermi-Ulam `ping-pong' problem
• Two-dimensional ‘discrete hydrodynamics’ and Monge–Ampère equations
• Jump in adiabatic invariant at a transition between modes of motion for systems with impacts
• On the Origin of the Cosmic Radiation

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