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Volume 9
Issue 16
10.3390/math9161993
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Article

The Hamilton–Jacobi Theory for Contact Hamiltonian Systems

by
Manuel de León
1,2,
Manuel Lainz
1,* and
Álvaro Muñiz-Brea
1
1
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/Nicolás Cabrera, 13-15, 28049 Madrid, Spain
2
Real Academia de Ciencias, C/Valverde 22, 28004 Madrid, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(16), 1993; https://doi.org/10.3390/math9161993
Submission received: 5 July 2021 / Revised: 13 August 2021 / Accepted: 15 August 2021 / Published: 20 August 2021
(This article belongs to the Special Issue New Trends in Hamilton-Jacobi Theory: Conservative and Dissipative Dynamics)
Versions Notes

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.
Keywords: contact Hamiltonian systems; Hamilton–Jacobi theory; contact evolution vector fields contact Hamiltonian systems; Hamilton–Jacobi theory; contact evolution vector fields

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MDPI and ACS Style

de León, M.; Lainz, M.; Muñiz-Brea, Á. The Hamilton–Jacobi Theory for Contact Hamiltonian Systems. Mathematics 2021, 9, 1993. https://doi.org/10.3390/math9161993

AMA Style

de León M, Lainz M, Muñiz-Brea Á. The Hamilton–Jacobi Theory for Contact Hamiltonian Systems. Mathematics. 2021; 9(16):1993. https://doi.org/10.3390/math9161993

Chicago/Turabian Style

de León, Manuel, Manuel Lainz, and Álvaro Muñiz-Brea. 2021. "The Hamilton–Jacobi Theory for Contact Hamiltonian Systems" Mathematics 9, no. 16: 1993. https://doi.org/10.3390/math9161993

APA Style

de León, M., Lainz, M., & Muñiz-Brea, Á. (2021). The Hamilton–Jacobi Theory for Contact Hamiltonian Systems. Mathematics, 9(16), 1993. https://doi.org/10.3390/math9161993

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