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,...

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Detalles Bibliográficos
Autores: Meson, Alejandro Mario, Vericat, Fernando
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/23655
Acceso en línea:http://hdl.handle.net/11336/23655
Access Level:acceso abierto
Palabra clave:TOPOLOGICAL ENTROPY
V-STATISTICS
MILTIFRACTAL SPECTRA
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.