On Estimations of the Generalized Hausdorff Dimension

G. A. Leonov, A. A. Florinskii

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract: This study presents the definition of an abstract homogeneous dimensional space with a finite compactness index, the definition of the Hausdorff–Besicovitch dimension spectrum of such a space, a theorem on the Hausdorff–Besicovitch spectrum values for its subspaces, and a number of results related to these concepts. Estimates are given for the dimension of sets that allow a mapping of a contracting type onto themselves. These estimates are an abstract version of the results close to the Douady–Oesterle theorem on the dimension of attractors of smooth dynamical systems in Euclidean spaces.

Original languageEnglish
Pages (from-to)327-333
Number of pages7
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number4
DOIs
StatePublished - 1 Oct 2019

Scopus subject areas

  • Mathematics(all)

Keywords

  • Hausdorff–Besicovitch dimension spectrum
  • Hausdorff–Lebesgue measure like functional
  • homogeneous dimensional space with finite index of compactness

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