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 …

arxiv:1811.03367v1 [math.SG] 8 Nov 2018 Page 1 arxiv:1811.03367v1 [math.SG] 8 Nov 2018
CONTACT HAMILTONIAN SYSTEMS MANUEL LAINZ VALCÁZAR AND MANUEL DE LEÓN …

Geodesic vector fields and other distinguished vector fields on a Riemann manifold were
used in the study of free motions on such a manifold, and we applied the geometric Hamilton …

This work is devoted to review the modern geometric description of the Lagrangian and
Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” …

We study the geometry underlying mechanics and its application to describe autonomous
and nonautonomous conservative dynamical systems of different types; as well as …

In this paper, we develop a Hamilton–Jacobi theory for forced Hamiltonian and Lagrangian
systems. We study the complete solutions, particularize for Rayleigh systems, and present …

The geometric framework for the Hamilton-Jacobi theory developed in the studies of
Cariñena et al.[Int. J. Geom. Methods Mod. Phys. 3 (7), 1417–1458 (2006)], Cariñena et …

Recently, M. de León et al.(Campos et al., 2015) have developed a geometrical description
of Hamilton–Jacobi theory for multisymplectic field theory. In our paper we analyze in the …

In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian
dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel …

A generalization of classical mechanics is obtained from a complex parametrization of the
phase space. The formalism supports complex Hamiltonian functions describing non …