THE STABILITY OF HAUSDORFF DIMENSION FOR THE LEVEL SETS UNDER THE PERTURBATION OF CONFORMAL REPELLERS

Lan Xu

doi:10.11948/2156-907X.20180349

2019 Volume 9 Issue 3

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Lan Xu. THE STABILITY OF HAUSDORFF DIMENSION FOR THE LEVEL SETS UNDER THE PERTURBATION OF CONFORMAL REPELLERS[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1120-1131. doi: 10.11948/2156-907X.20180349

Citation:

Lan Xu. THE STABILITY OF HAUSDORFF DIMENSION FOR THE LEVEL SETS UNDER THE PERTURBATION OF CONFORMAL REPELLERS[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 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^1, ,

1.
Department of Mathematics and Physics, Suzhou Vocational University, Suzhou, Jiangsu 215104, China

Corresponding author: Email address: xlan@jssvc.edu.cn(L. Xu)
Fund Project: The author is supported by National Natural Science Foundation of China (No.11871361)

Abstract

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 $.
- Hausdorff dimension /
- conformal repellers /
- topological pressure /
- multifractal analysis
MSC: 37C05, 37C45

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References

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