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Escaping orbits are rare in the quasi-periodic Fermi–Ulam ping-pong

Part of: Nonlinear dynamics Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Hamiltonian and Lagrangian mechanics Low-dimensional dynamical systems Ergodic theory

Published online by Cambridge University Press:  06 September 2018

MARKUS KUNZE  and
RAFAEL ORTEGA
MARKUS KUNZE
Affiliation:
Universität Köln, Institut für Mathematik, Weyertal 86–90, D-50931 Köln, Germany email mkunze@mi.uni-koeln.de
RAFAEL ORTEGA
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain email rortega@ugr.es
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Abstract

We consider the quasi-periodic Fermi–Ulam ping-pong model with no diophantine condition on the frequencies and show that typically the set of initial data which leads to escaping orbits has Lebesgue measure zero.

Keywords

Fermi accelerationquasi-periodic forcingdiophantine condition

MSC classification

Primary: 37J25: Stability problems 37E40: Twist maps 70H11: Adiabatic invariants
Secondary: 37A05: Measure-preserving transformations 70K40: Forced motions
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 4 , April 2020 , pp. 975 - 991
Copyright
© Cambridge University Press, 2018

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