A Note On Topological Conjugacy For Perpetual Points
Dynamical Systems
2015-11-20 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.1511.05836,
title = {A Note On Topological Conjugacy For Perpetual Points},
author = {Awadhesh Prasad},
journal= {arXiv preprint arXiv:1511.05836},
year = {2015}
}