On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions

Ya B. Pesin

doi:10.1007/BF01058436

On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions

Ya B. Pesin

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

We consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as Hausdorff dimension, box dimension, etc. We also introduce different ways to define and study the generalized spectrum for dimensions-a one-parameter family of characteristics of dimension type.

Original language	English (US)
Pages (from-to)	529-547
Number of pages	19
Journal	Journal of Statistical Physics
Volume	71
Issue number	3-4
DOIs	https://doi.org/10.1007/BF01058436
State	Published - May 1993

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01058436

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On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions

Abstract

All Science Journal Classification (ASJC) codes

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