A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

Román-Roy Narciso

doi:10.3934/jgm.2020009

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2020, Volume 12, Issue 3: 541-551. Doi: 10.3934/jgm.2020009

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A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

Román-Roy Narciso

Departament of Mathematics. Universidad Politécnica de Cataluña, Edificio C-3, Campus Norte UPC. C/ Jordi Girona 1. 08034 Barcelona, Spain

Received: March 31, 2019

Revised: November 30, 2019

Early access: March 2020

Published: September 2020

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Abstract

A complete geometric classification of symmetries of autonomous Hamiltonian systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.

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Mathematics Subject Classification: Primary: 37K05, 70H05, 70S10; Secondary: 37J15, 53D05, 70S05.

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