Homoclinic and heteroclinic orbits in Lagrangian dynamical systems

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Homoclinic and heteroclinic orbits in Lagrangian dynamical systems

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Yu, Guowei

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2013-05

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Abstract

In this thesis, variational methods are used to study the existence of homoclinic and heteroclinic orbits in various contexts of Lagrangian dynamical systems: 1. Monotone twist maps, which can be presented as time-one maps of certain positive definite time-periodic Lagrangian systems whose configuration spaces are 1-dim tori. 2. Time-periodic Tonelli Lagrangian systems whose configuration spaces are finite dimensional closed (i.e., compact, boundaryless) and connected smooth Riemannian manifolds. 3. Time-independent Tonelli Lagrangian systems whose configuration spaces are a 2-dim tori.

Keywords

Heteroclinic orbits

Homoclinic orbits

Lagrangian dynamics

Description

University of Minnesota Ph.D. dissertation. May 2013. Major: Mathematics. Advisor: Richard Moeckel. 1 computer file (PDF); vi, 118 pages.

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Yu, Guowei. (2013). Homoclinic and heteroclinic orbits in Lagrangian dynamical systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/156525.

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