In this survey, we review the classical Hamilton–Jacobi theory from a geometric point of view
in different geometric backgrounds. We propose a Hamilton–Jacobi equation for different …

We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the
one dominating in the literature, serves also for non-trivial contact structures. In this …

In this paper we study coisotropic reduction in different types of dynamics according to the
geometry of the corresponding phase space. The relevance of coisotropic reduction is …

This paper contains a fully geometric formulation of the General Equation for Non-
Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the …

The aim of this paper is to develop a Hamilton–Jacobi theory for contact Hamiltonian
systems. We find several forms for a suitable Hamilton–Jacobi equation accordingly to the …

We are proposing Tulczyjew's triple for contact dynamics. The most important ingredients of
the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse …

We describe a method, based on contact topology, of showing the existence of semi-infinite
trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and …

This work applies the contact formalism of classical mechanics and classical field theory,
introduced by Herglotz and later developed in the context of contact geometry, to describe …

In the contact-geometric formulation of classical thermodynamics distinction is made
between the energy and entropy representation. This distinction can be resolved by taking …

Contact Hamiltonian systems are a generalization of the Hamiltonian systems of classical
mechanics. The action is added as an extra variable in phase space, and symplectic …