The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

L. Asselle; G. Benedetti

doi:10.1142/S1793525316500205

The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

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Abstract

© 2016 World Scientific Publishing Company.Let M be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian H: T∗M → ℝ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if M is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of H.

Original language	English
Pages (from-to)	545-570
Journal	Journal of Topology and Analysis
Volume	8
Issue number	3
DOIs	https://doi.org/10.1142/S1793525316500205
Publication status	Published - 1 Sept 2016
Externally published	Yes

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title = "The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles",

abstract = "{\textcopyright} 2016 World Scientific Publishing Company.Let M be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian H: T∗M → ℝ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if M is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of H.",

author = "L. Asselle and G. Benedetti",

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T1 - The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

AU - Asselle, L.

AU - Benedetti, G.

PY - 2016/9/1

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N2 - © 2016 World Scientific Publishing Company.Let M be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian H: T∗M → ℝ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if M is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of H.

AB - © 2016 World Scientific Publishing Company.Let M be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian H: T∗M → ℝ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if M is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of H.

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DO - 10.1142/S1793525316500205

M3 - Article

SN - 1793-5253

VL - 8

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EP - 570

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 3

ER -

The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

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