# American Institute of Mathematical Sciences

January  2013, 33(1): 345-357. doi: 10.3934/dcds.2013.33.345

## Instability of periodic minimals

Received  September 2011 Revised  December 2011 Published  September 2012

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. Examples are well-known of stable periodic minimizers, but instability always holds for periodic solutions which are minimal in the sense of Aubry-Mather.
Citation: Antonio J. Ureña. Instability of periodic minimals. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 345-357. doi: 10.3934/dcds.2013.33.345
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