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The stability of Hausdorff dimension for the level sets under the perturbation of conformal repellers
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Keywords:Hausdorff dimension, conformal repellers, topological pressure, multifractal analysis
      Let M be a C^∞ compact Riemann manifold. f : M → M is a C^1 map and Λ_f ⊂ M is a conformal repeller of f. Suppose φ : M → 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 φ with respect to f_k and f.