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arXiv · 1511.05836

A Note On Topological Conjugacy For Perpetual Points

Awadhesh Prasad
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Abstract

Recently a new class of critical points, termed as {\sl perpetual points}, where acceleration becomes zero but the velocity remains non-zero, is observed in nonlinear dynamical systems. In this work we show whether a transformation also maps the perpetual points to another system or not. We establish mathematically that a linearly transformed system is topologicaly conjugate, and hence does map the perpetual points. However, for a nonlinear transformation, various other possibilities are also discussed. It is noticed that under a linear diffeomorphic transformation, perpetual points are mapped, and accordingly, eigenvalues are preserved.

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Awadhesh Prasad. 2015-11-17. A Note On Topological Conjugacy For Perpetual Points. https://arxiv.org/abs/1511.05836

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