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2002•Acta Scientiarum Naturalium Universitatis SunyatseniRequires access

A Note on the Dynamical System Defined on A Self-similar Set Satisfying SSC

Zhou Zuo-ling

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Abstract

A classical result says, for a self-similar set satisfying the strong separation condition,one can define a continuous self-mapping on it with the normalized Hausdorff measure of the self-similar set as its invariant ergodic measure.A necessary and sufficient condition for the normalized Hausdorff measure to be a measure with maximal entropy for the self-mapping is given.

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What this paper is about

A classical result says, for a self-similar set satisfying the strong separation condition,one can define a continuous self-mapping on it with the normalized Hausdorff measure of the self-similar set as its invariant ergodic measure.A necessary and sufficient condition for the normalized Hausdorff measure to be a measure with maximal entropy for the self-mapping is given.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A classical result says, for a self-similar set satisfying the strong separation condition,one can define a continuous self-mapping on it with the normalized Hausdorff measure of the self-similar set as its invariant ergodic measure.A necessary and sufficient condition for the normalized Hausdorff measure to be a measure with maximal entropy for the self-mapping is given.

Key concepts: Outer measure, Mathematics, Hausdorff measure, σ-finite measure, Invariant measure, Measure (data warehouse), Ergodic theory, Hausdorff dimension

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