Research output: Contribution to journal › Article › peer-review
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 language | English |
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Pages (from-to) | 327-333 |
Number of pages | 7 |
Journal | Vestnik St. Petersburg University: Mathematics |
Volume | 52 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2019 |
ID: 52494829