Limitation of Perpetual Points for Confirming Conservation in Dynamical Systems

Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a hypothesis that these points can determine whether a system is dissipative or not. This paper demonstrates that this hypothesis is not true since there are counterexamples. Furthermore, we explain that it is impossible to determine dissipation of a system based only on the structure of the system and its equations.

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