QUASI-SELF-SIMILAR FRACTALS CONTAINING “Y” HAVE DIMENSION LARGER THAN ONE

Angela Wu; Insung Park

doi:10.3934/dcds.2023138

QUASI-SELF-SIMILAR FRACTALS CONTAINING “Y” HAVE DIMENSION LARGER THAN ONE

Angela Wu
, Insung Park

Mathematical Science Institute

Indiana University Bloomington

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

1 Scopus citations

Abstract

Suppose X is a compact connected metric space and f: X → X is a metric coarse expanding conformal map in the sense of Haïssinsky-Pilgrim. We show that if X contains a homeomorphic copy of the letter “Y”, then the Hausdorff dimension of X is greater than one. As an application, we show that for a semi-hyperbolic rational map f its Julia set J_f is quasi-symmetric equivalent to a space having Hausdorff dimension 1 if and only if J_f is homeomorphic to a circle or a closed interval.

Original language	English
Pages (from-to)	1073-1086
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	44
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2023138
State	Published - Apr 2024

Keywords

Hausdorff dimension
Julia set
coarse expanding conformal map
conformal dimension
holomorphic dynamics

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10.3934/dcds.2023138

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KW - Hausdorff dimension

KW - Julia set

KW - coarse expanding conformal map

KW - conformal dimension

KW - holomorphic dynamics

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IS - 4

ER -

QUASI-SELF-SIMILAR FRACTALS CONTAINING “Y” HAVE DIMENSION LARGER THAN ONE

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