TY - JOUR

T1 - KAM theory for particles in periodic potentials

AU - Levi, Mark

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1990/12

Y1 - 1990/12

N2 - 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 L 1; 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.

AB - 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 L 1; 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.

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U2 - 10.1017/S0143385700005897

DO - 10.1017/S0143385700005897

M3 - Article

AN - SCOPUS:84971946620

SN - 0143-3857

VL - 10

SP - 777

EP - 785

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 4

ER -