Fractal Dimensions for Dissipative Sets

Bernd O Stratmann; R Vogt

doi:10.1088/0951-7715/10/2/014

Fractal Dimensions for Dissipative Sets

Bernd O Stratmann, R Vogt

Pure Mathematics

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

Abstract

For characteristic subsets of infinite binary shift spaces, we derive lower bounds for the Hausdorff dimension with respect to Gibbs measures. Using these estimates, we then obtain a more refined fractal analysis of dissipative phenomena for the dynamical system which inspired van Strien and Nowicki to construct Julia sets of positive Lebesgue measure.

Original language	English
Pages (from-to)	565-577
Number of pages	13
Journal	Nonlinearity
Volume	10
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/10/2/014
Publication status	Published - Mar 1997

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title = "Fractal Dimensions for Dissipative Sets",

abstract = "For characteristic subsets of infinite binary shift spaces, we derive lower bounds for the Hausdorff dimension with respect to Gibbs measures. Using these estimates, we then obtain a more refined fractal analysis of dissipative phenomena for the dynamical system which inspired van Strien and Nowicki to construct Julia sets of positive Lebesgue measure.",

author = "Stratmann, \{Bernd O\} and R Vogt",

year = "1997",

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doi = "10.1088/0951-7715/10/2/014",

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T1 - Fractal Dimensions for Dissipative Sets

AU - Stratmann, Bernd O

AU - Vogt, R

PY - 1997/3

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AB - For characteristic subsets of infinite binary shift spaces, we derive lower bounds for the Hausdorff dimension with respect to Gibbs measures. Using these estimates, we then obtain a more refined fractal analysis of dissipative phenomena for the dynamical system which inspired van Strien and Nowicki to construct Julia sets of positive Lebesgue measure.

UR - https://www.scopus.com/pages/publications/0041729768

UR - http://stacks.iop.org/Non/10/565

U2 - 10.1088/0951-7715/10/2/014

DO - 10.1088/0951-7715/10/2/014

M3 - Article

SN - 0951-7715

VL - 10

SP - 565

EP - 577

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

Fractal Dimensions for Dissipative Sets

Abstract

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