Stability of Periodic Orbits by Conley-Zehnder index theory

preprint2018arXivOpen access

Abstract

We give a necessary and sufficient condition for strong stability of low dimensional Hamiltonian systems, in terms of the iterates of a closed orbit and the Conley-Zehnder index. Applications to Mathieu equation and stable harmonic oscillations for forced pendulum type equations are considered as applications of the main result.

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