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

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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 languageEnglish (US)
Pages (from-to)529-547
Number of pages19
JournalJournal of Statistical Physics
Volume71
Issue number3-4
DOIs
StatePublished - May 1 1993

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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