# Lectures on the free period Lagrangian action functional

@article{Abbondandolo2013LecturesOT, title={Lectures on the free period Lagrangian action functional}, author={Alberto Abbondandolo}, journal={Journal of Fixed Point Theory and Applications}, year={2013}, volume={13}, pages={397-430} }

In this expository article we study the question of the existence of periodic orbits of prescribed energy for classical Hamiltonian systems on compact configuration spaces.We use a variational approach, by studying how the behavior of the free period Lagrangian action functional changes when the energy crosses certain values, known as the Mañé critical values.

## 32 Citations

Linear instability of periodic orbits of free period Lagrangian systems

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In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general…

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These notes were prepared in occasion of a mini-course given by the author at the “CIMPA Research School Hamiltonian and Lagrangian Dynamics” (10–19 March 2015 Salto, Uruguay). The talks were meant…

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Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the…

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This paper studies the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal boundary conditions and that lay on the boundary only in their extreme points.

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Let $Q$ be a closed manifold admitting a locally free action of a compact Lie group $G$. In this paper, we study the properties of geodesic flows on $Q$ given by suitable G-invariant Riemannian…

Minimal Boundaries in Tonelli Lagrangian Systems

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We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface $M$. More specifically, we show that for every energy larger…

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We show that on a closed Riemannian manifold with fundamental group isomorphic to Z, other than the circle, every isometry that is homotopic to the identity possesses infinitely many invariant…

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