Expanding direction of the period doubling operator
Dynamical Systems
2016-09-06 v1
Abstract
We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a ``Perron-Frobenius type operator'', to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced operator. The proof is constructive. One can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point.
Keywords
Cite
@article{arxiv.math/9201281,
title = {Expanding direction of the period doubling operator},
author = {Yunping Jiang and Takehiko Morita and Dennis Sullivan},
journal= {arXiv preprint arXiv:math/9201281},
year = {2016}
}