Period tripling and quintupling renormalizations below C2 space
Abstract
In this paper, we explore the period tripling and period quintupling renormalizations below C2 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 C1+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 C1+Lip unimodal maps have unbounded topological entropy.