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The periodic orbits problem in Tonelli Hamiltonian dynamics

Introductory Workshop: Hamiltonian systems, from topology to applications through analysis August 20, 2018 - August 24, 2018

August 24, 2018 (09:00 AM PDT - 09:30 AM PDT)
Speaker(s): Marco Mazzucchelli (École Normale Supérieure de Lyon)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Tonelli Hamiltonian

  • periodic orbits

  • closed geodesics

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

Abstract

My talk will be an introductory lecture on the periodic orbits problem for Tonelli Hamiltonian systems. In a first part of the talk, I will recall the variational formulation of the problem, and its connections to Aubry-Mather theory and Weak KAM theory. I will then review some of the main known results on the multiplicity of periodic orbits with prescribed energy, and some of the celebrated open questions in the field, including the closed geodesics problem in Riemannian and Finsler manifolds.

Supplements
32040?type=thumb Notes 691 KB application/pdf Download
Video/Audio Files

15-Mazzucchelli

H.264 Video 15-Mazzucchelli.mp4 383 MB video/mp4 Download
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