Renormalization group structure for sums of variables generated by incipiently chaotic maps

We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in cont...

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Detalles Bibliográficos
Autores: Fuentes, Miguel Angel, Robledo, Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/124980
Acceso en línea:http://hdl.handle.net/11336/124980
Access Level:acceso abierto
Palabra clave:NONLINEAR DYNAMICS
RENORMALIZATION GROUP
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
Descripción
Sumario:We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.