Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical aspects of contact mechanical systems and field theories   Many important theories in modern physics can be stated using differential
geometry. Symplectic geometry is the natural framework to deal with autonomous
Hamiltonian mechanics. This admits several generalizations for nonautonomous
systems, both regular and singular. Some of these extensions are the subject of
this thesis.
  Recently there has been a growing interest in studying dissipative mechanical
systems from a geometric perspective using contact geometry. In this thesis we
review what has been done in this topic and go deeper, studying symmetries and
dissipated quantities of contact systems, and developing the Skinner-Rusk
formalism for these systems.
  With regard to classical field theory, we introduce the notion of
k-precosymplectic manifold and use it to give a geometric description of
singular nonautonomous field theories. We also devise a constraint algorithm
for these systems.
  Field theories with damping are described through a modification of the De
Donder-Weyl Hamiltonian field theory. This is achieved by combining contact
geometry and k-symplectic structures, resulting in the k-contact formalism. We
introduce two notions of dissipation laws, generalizing the concept of
dissipated quantity. These developments are also applied to Lagrangian field
theory. The Skinner-Rusk formulation for k-contact systems is described in
detail and we show how to recover the Lagrangian and Hamiltonian formalisms
from it.
  Throughout the thesis we present several examples in mechanics and field
theory. The most remarkable mechanical examples are the damped harmonic
oscillator, the motion in a gravitational field with friction, the parachute
equation and the damped simple pendulum. In field theory, we study the damped
vibrating string, the Burgers' equation, the Klein-Gordon equation and its
relation with the telegrapher's equation, and the Maxwell's equations with
dissipation.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs