Yu, Guowei2013-09-102013-09-102013-05https://hdl.handle.net/11299/156525University of Minnesota Ph.D. dissertation. May 2013. Major: Mathematics. Advisor: Richard Moeckel. 1 computer file (PDF); vi, 118 pages.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.en-USHeteroclinic orbitsHomoclinic orbitsLagrangian dynamicsThesis or Dissertation