Geometrical structures of higher-order dynamical systems and field theories
arXiv:1410.7825
Abstract
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.
Ph.D. Thesis at Universitat Politècnica de Catalunya - BarcelonaTech. 256 pages. Acknowledgments have been removed with respect to the original version. Qualification: Excellent Cum Laude