Oscillating mushrooms: adiabatic theory for a non-ergodic system
Author(s)
Gelfreich, V
Rom-Kedar, V
Turaev, D
Type
Journal Article
Abstract
Can elliptic islands contribute to sustained energy growth as parameters of a
Hamiltonian system slowly vary with time? In this paper we show that a mushroom
billiard with a periodically oscillating boundary accelerates the particle
inside it exponentially fast. We provide an estimate for the rate of
acceleration. Our numerical experiments confirms the theory. We suggest that a
similar mechanism applies to general systems with mixed phase space.
Hamiltonian system slowly vary with time? In this paper we show that a mushroom
billiard with a periodically oscillating boundary accelerates the particle
inside it exponentially fast. We provide an estimate for the rate of
acceleration. Our numerical experiments confirms the theory. We suggest that a
similar mechanism applies to general systems with mixed phase space.
Date Issued
2014-09-16
Citation
Journal of Physics A - Mathematical and Theoretical, 2014, 47 (39)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A - Mathematical and Theoretical
Volume
47
Issue
39
Copyright Statement
© The Authors 2014. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Identifier
http://arxiv.org/abs/1305.2624v1
Subjects
math.DS
math.DS
37D50, 82C05, 70H11
Publication Status
Published