Mathematics (Aug 2021)

The Hamilton–Jacobi Theory for Contact Hamiltonian Systems

  • Manuel de León,
  • Manuel Lainz,
  • Álvaro Muñiz-Brea

DOI
https://doi.org/10.3390/math9161993
Journal volume & issue
Vol. 9, no. 16
p. 1993

Abstract

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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.

Keywords