The Hamilton-Jacobi theory for contact hamiltonian systems

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 Hamiltonian and the evolution vector fields for a given Hamiltonian function. We also analyze the corresponding formulation on the symplectification of the contact Hamiltonian system, and establish the relations between these two approaches. In the last section, some examples are discussed.We acknowledge the financial support from the MINECO Grant PID2019- 106715GB-C21. Manuel Laínz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. Álvaro Muñiz thanks ICMAT for the “Grant Programme Severo Ochoa–ICMAT: Introduction to Research 2020” and Fundación Barrié for its fellowship for postgraduate studie