• Corpus ID: 118962012

Packing dimensions of the divergence points of self-similar measures with the open set condition

@article{Zhou2012PackingDO,
  title={Packing dimensions of the divergence points of self-similar measures with the open set condition},
  author={Xiaoyao Zhou and Ercai Chen},
  journal={arXiv: Dynamical Systems},
  year={2012}
}
Let µ be the self-similar measure supported on the self- similar set K with open set condition. In this article, we discuss the packing dimension of the set {x ∈ K : A( log µ(B(x,r)) logr ) = I} for 
1 Citations
Inverse Problems in Multifractal Analysis
We present recent results regarding the construction of positive measures with a prescribed multifractal nature, as well as their counterpart in multifractal analysis of Holder continuous functions.

References

SHOWING 1-10 OF 17 REFERENCES
The pointwise dimension of self-similar measures
The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist
Hausdorff dimensions of the divergence points of self-similar measures with the open set condition
Let μ be the self-similar measure supported on the self-similar set K with the open set condition. For x K, let A(D(x)) denote the set of accumulation points of as r 0. In this paper, we show that
Random Self-Similar Multifractals
TLDR
For describing the local structure of a random self-similar measure, the multi-fractal decomposition of its support into sets of points of different local dimension is used and the Hausdorff dimensions of these sets are computed.
Self-Conformal Multifractal Measures
A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper we describe the local structure of self-conformal measures. For such a measure we divide its support
Divergence points of self-similar measures and packing dimension
Divergence points of self-similar measures satisfying the OSC☆
Normal and Non-Normal Points of Self-Similar Sets and Divergence Points of Self-Similar Measures
Let K and μ be the self‐similar set and the self‐similar measure associated with an IFS (iterated function system) with probabilities (Si, pi)i=1,…,N satisfying the open set condition. Let Σ={1,…,N}N
Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages
Ergodic Limits on the Conformal Repellers
Abstract Let J be the repeller of an expanding, C1+δ-conformal topological mixing map g. Let Φ:J→ R d be a continuous function and let α(x)=limn→∞ 1 n ∑n−1j=0Φ(gjx) (when the limit exists) be the
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