Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Prasad, Awadhesh
Institution: University of Delhi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2178245489