On the topological entropy of the irregular part of v-statistics multifractal spectra
Let (x, d) be a compact metric space and f : x → x, if xr is the product of r−copies of x, r ≥ 1, and φ : xr → r, then the multifractal decomposition for v −statistics is given by eφ (α) = ( x : lim n→∞ 1 nr p 0≤i1≤...≤ir≤n−1 φ ¡ f i1 (x) , ..., fir (x) ¢ = α ) . The irregular part, or historic set,...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2013 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/23655 |
| Acesso em linha: | http://hdl.handle.net/11336/23655 |
| Access Level: | Acceso aberto |
| Palavra-chave: | TOPOLOGICAL ENTROPY V-STATISTICS MILTIFRACTAL SPECTRA https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let (x, d) be a compact metric space and f : x → x, if xr is the product of r−copies of x, r ≥ 1, and φ : xr → r, then the multifractal decomposition for v −statistics is given by eφ (α) = ( x : lim n→∞ 1 nr p 0≤i1≤...≤ir≤n−1 φ ¡ f i1 (x) , ..., fir (x) ¢ = α ) . The irregular part, or historic set, of the spectrum is the set points x ∈ x, for which the limit does not exist. In this article we prove that for dynamical systems with specification, the irregular part of the v −statistics spectrum has topological entropy equal to that of the whole space x. |
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