On the connections between symmetries and conservation rules of dynamical systems |
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Authors: | Giampaolo Cicogna |
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Affiliation: | Dipartimento di Fisica, Università di Pisa and INFN, Sezione di Pisa, , 56127 Pisa, Italy |
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Abstract: | The strict connection between Lie point‐symmetries of a dynamical system and its constants of motion is discussed and emphasized through old and new results. It is shown in particular how the knowledge of the symmetry of a dynamical system can allow us to obtain conserved quantities that are invariant under the symmetry. In the case of Hamiltonian dynamical systems, it is shown that if the system admits a symmetry of a ‘weaker’ type (specifically, a λ or a Λ‐symmetry), then the generating function of the symmetry is not a conserved quantity, but the deviation from the exact conservation is ‘controlled’ in a well‐defined way. Several examples illustrate the various aspects. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | dynamical systems Lie point‐symmetries λ ‐symmetries constants of motion Hamiltonian dynamical systems |
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