On Estimations of the Generalized Hausdorff Dimension
- Authors: Leonov G.A.1, Florinskii A.A.1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 52, No 4 (2019)
- Pages: 327-333
- Section: To the Memory of G.a. Leonov
- URL: https://journals.rcsi.science/1063-4541/article/view/186421
- DOI: https://doi.org/10.1134/S106345411904006X
- ID: 186421
Cite item
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.
About the authors
G. A. Leonov
St. Petersburg State University
Email: florinskiy.a@gmail.com
Russian Federation, St. Petersburg, 199034
A. A. Florinskii
St. Petersburg State University
Author for correspondence.
Email: florinskiy.a@gmail.com
Russian Federation, St. Petersburg, 199034