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Invariant curves and time-dependent potentials

Published online by Cambridge University Press:  19 September 2008

Stephane Laederich and
Mark Lev
Stephane Laederich
Affiliation:
Department of Mathematics, Boston University, Boston, MA 02215, USA
Mark Lev
Affiliation:
Department of Mathematics, Boston University, Boston, MA 02215, USA
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Abstract

In this paper we prove the existence of invariant curves and thus stability for all time for a class of Hamiltonian systems with time-dependent potentials, namely, for systems of the form

where

is a superquadratic polynomial potential with periodic coefficients. As a limiting case, a proof of the stability of Ulam's problem of a particle bouncing between two periodicially moving walls is given.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991, pp. 365 - 378
Copyright
Copyright © Cambridge University Press 1991

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References

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