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arXiv · 1802.01361

Measure-preserving symmetries and reversibilities of ordinary differential systems

Marco Sabatini
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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 Li\'enard systems.

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Marco Sabatini. 2018-02-05. Measure-preserving symmetries and reversibilities of ordinary differential systems. https://arxiv.org/abs/1802.01361

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