| 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. |
