Title: Period tripling and quintupling renormalizations below C^2 Space

Authors: Rohit Kumar and V.V.M.S. Chandramouli

Journal: Discrete & Continuous Dynamical Systems -A (DCDS-A) Volume: 41 (12)

Year: 2021

Publisher: American Institute of Mathematical Sciences

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.