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oai:recercat.cat:2117/3631982026-02-06T04:26:45Zcom_2072_1033col_2072_452950

A summary on symmetries and conserved quantities of autonomous Hamiltonian systems Román Roy, Narciso Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències Nonlinear systems Hamiltonian systems Field theory (Physics) Symmetries Conserved quantities Hamiltonian systems 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 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. I acknowledge the financial support from the Spanish Ministerio de Econom´ıa y Competitividad project MTM2014–54855–P, the Ministerio de Ciencia, Innovaci´on y Universidades project PGC2018-098265-BC33, and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017–SGR–932. I also greatly appreciate the comments and suggestions of Prof. Mikhail S. Plyushchay. Finally, my thanks to the referees for their extensive and valuable comments that have allowed me to significantly improve the final version of the work. Postprint (author's final draft) 2020 Article Roman-Roy, N. A summary on symmetries and conserved quantities of autonomous Hamiltonian systems. "Journal of Geometric Mechanics", 2020, vol. 12, núm. 3, p. 541-551. 1941-4897 https://hdl.handle.net/2117/363198 10.3934/jgm.2020009 eng http://www.aimsciences.org/article/doi/10.3934/jgm.2020009 https://creativecommons.org/licenses/by/4.0/ Open Access Attribution 4.0 International 11 p. application/pdf AMER INST MATHEMATICAL SCIENCES-AIMS