We prove that measure-preserving symmetries of an n-dimensional differential system preserve its divergence and the divergence derivatives along the solutions. Also, we prove that measure-preserving reversibilities preserve odd-order divergence derivatives along the solutions, and that even-order derivatives are multiplied by -1. We apply such results to find all the area-preserving symmetries and reversibilities of planar Lotka-Volterra and Liénard systems.
Measure-preserving symmetries and reversibilities of ordinary differential systems / Sabatini, Marco. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - STAMPA. - 2020, 164:(2020). [10.1016/j.bulsci.2020.102906]
Measure-preserving symmetries and reversibilities of ordinary differential systems
Sabatini, Marco
2020-01-01
Abstract
We prove that measure-preserving symmetries of an n-dimensional differential system preserve its divergence and the divergence derivatives along the solutions. Also, we prove that measure-preserving reversibilities preserve odd-order divergence derivatives along the solutions, and that even-order derivatives are multiplied by -1. We apply such results to find all the area-preserving symmetries and reversibilities of planar Lotka-Volterra and Liénard systems.File | Dimensione | Formato | |
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SABATINI - Measure-preserving symmetries and reversibilities of ordinary differential systems.pdf
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