On Estimations of the Generalized Hausdorff Dimension
- 作者: Leonov G.1, Florinskii A.1
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隶属关系:
- St. Petersburg State University
- 期: 卷 52, 编号 4 (2019)
- 页面: 327-333
- 栏目: 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
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详细
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.
作者简介
G. Leonov
St. Petersburg State University
Email: florinskiy.a@gmail.com
俄罗斯联邦, St. Petersburg, 199034
A. Florinskii
St. Petersburg State University
编辑信件的主要联系方式.
Email: florinskiy.a@gmail.com
俄罗斯联邦, St. Petersburg, 199034