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The Hamilton–Jacobi Theory for Contact Hamiltonian Systems

Author

Listed:
  • Manuel de León

    (Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/Nicolás Cabrera, 13-15, 28049 Madrid, Spain
    Real Academia de Ciencias, C/Valverde 22, 28004 Madrid, Spain)

  • Manuel Lainz

    (Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/Nicolás Cabrera, 13-15, 28049 Madrid, Spain)

  • Álvaro Muñiz-Brea

    (Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/Nicolás Cabrera, 13-15, 28049 Madrid, Spain)

Abstract

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.

Suggested Citation

  • Manuel de León & Manuel Lainz & Álvaro Muñiz-Brea, 2021. "The Hamilton–Jacobi Theory for Contact Hamiltonian Systems," Mathematics, MDPI, vol. 9(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1993-:d:618415
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    Cited by:

    1. Oğul Esen & Cristina Sardón & Marcin Zajac, 2024. "A Discrete Hamilton–Jacobi Theory for Contact Hamiltonian Dynamics," Mathematics, MDPI, vol. 12(15), pages 1-24, July.

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