Matricial representation of period doubling cascade
Chaotic Dynamics
2010-01-19 v1
Abstract
Starting from the cycle permutation sigma_(2^k) associated with the (2^k)-periodic orbit of the period doubling cascade we obtain the inverse permutation (sigma_(2^k))^-1. Then we build a matrix permutation related to (sigma_(2^k))^-1, which includes the visiting order of the (2^k)-periodic orbit points. After some manipulations a recurrence relation of matricial representation of period doubling cascade is obtained. Finally the explicit matricial representation is reached.
Keywords
Cite
@article{arxiv.1001.3120,
title = {Matricial representation of period doubling cascade},
author = {Lucia Cerrada and Jesus San Martin},
journal= {arXiv preprint arXiv:1001.3120},
year = {2010}
}
Comments
20 pages and one figure