Author:
CHEN YURONG,LUO CHIYI,ZHAO YUN
Abstract
AbstractFor a$C^1$non-conformal repeller, this paper proves that there exists an ergodic measure of full Carathéodory singular dimension. For an average conformal hyperbolic set of a$C^1$diffeomorphism, this paper constructs a Borel probability measure (with support strictly inside the repeller) of full Hausdorff dimension. If the average conformal hyperbolic set is of a$C^{1+\alpha }$diffeomorphism, this paper shows that there exists an ergodic measure of maximal dimension.
Funder
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics