# High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces

@article{Abbondandolo2006HighAO, title={High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces}, author={Alberto Abbondandolo and Alessio Figalli}, journal={Journal of Differential Equations}, year={2006}, volume={234}, pages={626-653} }

## 27 Citations

Linear instability for periodic orbits of non-autonomous Lagrangian systems

- Mathematics
- 2019

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the…

Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces

- Mathematics
- 2009

Nontrivial solutions of superquadratic Hamiltonian systems with Lagrangian boundary conditions and the L-index theory

- Mathematics
- 2008

AbstractIn this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems $$
\dot z
$$(t) = J▽H(t, z(t)) with Lagrangian boundary conditions, where is a semipositive…

A Smooth Pseudo-Gradient for the Lagrangian Action Functional

- Mathematics
- 2008

Abstract We study the action functional associated to a smooth Lagrangian function on the tangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action…

Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits

- Mathematics
- 2019

We show the the existence of noncontractible periodic orbits for every compactly supported time-dependent Hamiltonian on the open unit disk cotangent bundle of a Finsler manifold provided that the…

Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index

- Mathematics
- 2007

Abstract.We study the properties of the asymptotic Maslov index of invariant measures for time-periodic Hamiltonian systems on the cotangent bundle of a compact manifold M. We show that if M has…

Morse index and linear stability of relative equilibria in singular mechanical systems

- Mathematics
- 2015

We have focussed on the study of the linear stability of some particular periodic orbits (called relative equilibria) in planar singular mechanical systems with SO(2)-symmetry, and we have achieved…

Periodic orbits in virtually contact structures

- MathematicsJournal of Topology and Analysis
- 2018

We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic…

On the energy functional on Finsler manifolds and applications to stationary spacetimes

- Mathematics
- 2007

In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under…

Linear instability of periodic orbits of free period Lagrangian systems

- Mathematics
- 2021

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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