Complete orbits for twist maps on the plane: extensions and applications

DOI10.1007/s10884-010-9185-yzbMath1228.37035OpenAlexW2076651544MaRDI QIDQ650166

Rafael Ortega, Markus Kunze

Publication date: 25 November 2011

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-010-9185-y

zbMATH Keywords

rotation numbertwist mapAubry-Mather orbit

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 (11)

On unbounded motions in a real analytic bouncing ball problem ⋮ Diffusion and chaos in a bouncing ball model ⋮ Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ Some remarks on the periodic motions of a bouncing ball ⋮ A \(C^{1+\alpha}\) mechanical counterexample to Moser's twist theorem ⋮ Twist Mappings with Non-Periodic Angles ⋮ Escaping orbits are also rare in the almost periodic Fermi-Ulam ping-pong ⋮ A mechanical counterexample to KAM theory with low regularity ⋮ 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 ⋮ Chaotic dynamics in an impact problem

Cites Work

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• Invariant tori and Lagrange stability of pendulum-type equations
• Bouncing balls in nonlinear potentials
• On the approximation of the elastic bounce problem on Riemannian manifolds
• Minimal functions with unbounded integral
• On Schauder's fixed point theorem and forced second-order nonlinear oscillations
• Complete orbits for twist maps on the plane
• KAM theory for particles in periodic potentials

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