Topics in contact Hamiltonian systems
The work of this thesis explores contact Hamiltonian systems as ageometrical setting to study physical systems with dissipation. Unlikesymplectic dynamical systems, contact Hamiltonian systems do notconserve energy, allowing the description of systems with differenttypes of dissipation and forcing.
In his thesis Federico Zadra provides background knowledge on contactmanifolds and introduces contact Hamiltonian systems with examples.Zadra focuses on numerical methods for contact Hamiltoniansystems, including geometry preserving integrators and deep learningtechniques. Zadra presents analytical results: thecomputation of the Baker-Campbell-Hausdorff formula for certainalgebras and the study of symmetry and integrability in contactHamiltonian systems. The thesis builds on previously published workand includes unpublished work in progress.