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Summary: Instability of periodic minimals
Antonio J. Ure~na
Dedicated to Jean Mawhin.
Abstract
We consider second-order Euler-Lagrange systems which are periodic in time. Their
periodic solutions may be characterized as the stationary points of an associated action
functional, and we study the dynamical implications of minimizing the action. Ex-
amples are well-known of stable periodic minimizers, but instability always holds for
periodic solutions which are minimal in the sense of Aubry-Mather.
Key words: Periodic minimizers, minimals, quasi-asymptotic solutions, instability.
1 Introduction
Consider the Euler-Lagrange equations
d
dt
[
xL
(
t, x(t), x(t)
)]
= xL
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