Interval maps quasi-symmetrically conjugate to a piecewise affine map

Abstract

Consider a multimodal interval map f of C 3 with non-flat critical points. We establish several characterizations of the map f is quasisymmetrically conjugated to a piecewise affine map in the case f is topologically exact and all of its periodic points are hyperbolic repelling. In particular, we give a negative answer to a question posted by Henk Bruin in [Bru96].2010 Mathematics Subject Classification. 37E05.