A Note On Topological Conjugacy For Perpetual Points
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1511.05836
- arXiv:
- arXiv:1511.05836
- Bibcode:
- 2015arXiv151105836P
- Keywords:
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- Mathematics - Dynamical Systems;
- Nonlinear Sciences - Chaotic Dynamics