Period tripling and quintupling renormalizations below $C^2$ space
Dynamical Systems
2021-07-09 v1
Abstract
In this paper, we explore the period tripling and period quintupling renormalizations below class of unimodal maps. We show that for a given proper scaling data there exists a renormalization fixed point on the space of piece-wise affine maps which are infinitely renormalizable. Furthermore, we show that this renormalization fixed point is extended to a unimodal map, considering the period tripling and period quintupling combinatorics. Moreover, we show that there exists a continuum of fixed points of renormalizations by considering a small variation on the scaling data. Finally, this leads to the fact that the tripling and quintupling renormalizations acting on the space of unimodal maps have unbounded topological entropy.
Cite
@article{arxiv.2010.01293,
title = {Period tripling and quintupling renormalizations below $C^2$ space},
author = {Rohit Kumar and V. V. M. S. Chandramouli},
journal= {arXiv preprint arXiv:2010.01293},
year = {2021}
}