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KAM theory for particles in periodic potentials

Published online by Cambridge University Press:  19 September 2008

Mark Levi
Mark Levi
Affiliation:
Department of Mathematics, Boston University, Boston, Mass. 02215, USA
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Abstract

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It is shown that the system of the form x + V′ (x) = p (t) with periodic V and p and with (p) = 0 is near-integrable for large energies. In particular, most (in the sense of Lebesgue measure) fast solutions are quasiperiodic, provided V ∈ C(5) and p ∈ L1; furthermore, for any solution x(t) there exists a velocity bound c for all time: |x(t)| < c for all t ∈ R. For any real number r there exists a solution with that average velocity, and when r is rational, this solution can be chosen to be periodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 4 , December 1990 , pp. 777 - 785
Copyright
Copyright © Cambridge University Press 1990

References

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