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Volume 9, Number 3, 2019, Pages 1120-1131                                                                DOI:10.11948/2156-907X.20180349
The stability of Hausdorff dimension for the level sets under the perturbation of conformal repellers
Lan Xu
Keywords:Hausdorff dimension, conformal repellers, topological pressure, multifractal analysis.
Abstract:
      Let $M$ be a $C^\infty$ compact Riemann manifold. $f:M\to M$ is a $C^1$ map and $\Lambda_f \subset M$ is a conformal repeller of $f$. Suppose $\varphi:M\to\mathbb{R}$ is a continuous function and let $f_k$ be nonconformal perturbation of the map $f$. We consider the stability of Hausdorff dimension of level sets for Birkhorff average of potential function $\varphi$ with respect to $f_k$ and $f$.
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