The integrability of the generalized Hamiltonian system

Authors

DOI:

https://doi.org/10.60063/gsu.fmi.111.55-76

Keywords:

complete integrability, contact transformations, generalized Hamiltonian system, Herglotz variational principle, integrability, integrable systems

Abstract

This paper reviews the generalized Hamiltonian system and its connection to contact transformations. The generalized Hamiltonian system is related to Herglotz variational principle in the same way in which the Hamiltonian system is related to the classical variational principle. We prove a criterion for the integrability of the generalized Hamiltonian system in terms of a complete set of first integrals, and a method of generating such first integrals. These results are due to Gustav Herglotz.

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Published

2024-12-04

How to Cite

Georgieva, B. (2024). The integrability of the generalized Hamiltonian system. Ann. Sofia Univ. Fac. Math. And Inf., 111, 55–76. https://doi.org/10.60063/gsu.fmi.111.55-76

Issue

Vol. 111 (2024): Ann. Sofia Univ. Fac. Math. and Inf.

Section

Articles