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arXiv · 2010.01293

Period tripling and quintupling renormalizations below $C^2$ space

Rohit Kumar·V. V. M. S. Chandramouli
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Abstract

In this paper, we explore the period tripling and period quintupling renormalizations below $C^2$ 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 $C^{1+Lip}$ 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 $C^{1+Lip}$ unimodal maps have unbounded topological entropy.

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Rohit Kumar, V. V. M. S. Chandramouli. 2020-10-03. Period tripling and quintupling renormalizations below $C^2$ space. https://doi.org/10.3934/dcds.2021091

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