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 …

Contact geometry allows us to describe some thermodynamic and dissipative systems. In
this paper we introduce a new geometric structure in order to describe time-dependent …

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 …

We prove that, under some natural conditions, Hamiltonian systems on a contact manifold C
can be split into a Reeb dynamics on an open subset of C and a Liouville dynamics on a …

We use a formulation of Noether's theorem for contact Hamiltonian systems to derive a
relation between the thermodynamic entropy and the Noether invariant associated with time …

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

In contact Hamiltonian systems, the so‐called dissipated quantities are akin to conserved
quantities in classical Hamiltonian systems. In this article, a Noether's theorem for non …

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 …

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent
and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems …