2018/02/05 by Marco Sabatini, Sabatini, Marco
Mathematics · Physics and Astronomy · #34C14 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #math.DS #msc:34C14
paper · pdf · doi:10.48550/arxiv.1802.01361
17 pages
arxiv created 2018/02/05 · openalex publication_date 2018/02/05 · arxiv updated 2018/02/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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.