A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

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 symplec...

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Detalhes bibliográficos
Autor: Román Roy, Narciso|||0000-0003-3663-9861
Tipo de documento: artigo
Data de publicação:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/363198
Acesso em linha:https://hdl.handle.net/2117/363198
https://dx.doi.org/10.3934/jgm.2020009
Access Level:Acceso aberto
Palavra-chave:Nonlinear systems
Hamiltonian systems
Field theory (Physics)
Symmetries
Conserved quantities
Noether theorem
Symplectic manifolds
Sistemes no lineals
Hamilton, Sistemes de
Camps, Teoria dels (Física)
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Descrição
Resumo: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.