On Estimations of the Generalized Hausdorff Dimension

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On Estimations of the Generalized Hausdorff Dimension. / Leonov, G. A.; Florinskii, A. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 4, 01.10.2019, p. 327-333.

Research output: Contribution to journal › Article › peer-review

Author

Leonov, G. A. ; Florinskii, A. A. / On Estimations of the Generalized Hausdorff Dimension. In: Vestnik St. Petersburg University: Mathematics. 2019 ; Vol. 52, No. 4. pp. 327-333.

BibTeX

@article{8a5f12a570c844edb7d1a5df9279a0fd,

title = "On Estimations of the Generalized Hausdorff Dimension",

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.",

keywords = "Hausdorff–Besicovitch dimension spectrum, Hausdorff–Lebesgue measure like functional, homogeneous dimensional space with finite index of compactness",

author = "Leonov, {G. A.} and Florinskii, {A. A.}",

year = "2019",

month = oct,

day = "1",

doi = "10.1134/S106345411904006X",

language = "English",

volume = "52",

pages = "327--333",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - On Estimations of the Generalized Hausdorff Dimension

AU - Leonov, G. A.

AU - Florinskii, A. A.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Hausdorff–Besicovitch dimension spectrum

KW - Hausdorff–Lebesgue measure like functional

KW - homogeneous dimensional space with finite index of compactness

UR - http://www.scopus.com/inward/record.url?scp=85077054898&partnerID=8YFLogxK

U2 - 10.1134/S106345411904006X

DO - 10.1134/S106345411904006X

M3 - Article

AN - SCOPUS:85077054898

VL - 52

SP - 327

EP - 333

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 52494829