Infinite Iterated Function Systems With Overlaps

Sze-Man Ngai

Infinite Iterated Function Systems With Overlaps

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

<p> We extend the weak separation condition to in&filig;nite iterated function systems of conformal contractions with overlaps. It turns out that there are two natural but di&fflig;erent extensions. We study the topological pressure functions associated with these separation conditions. We prove a dimension formula for the Hausdor&fflig; dimension of the limit sets under the bounded distortion property and these weak separation conditions. This is joint work with Ji-Xi Tong.</p>

Original language	American English
State	Published - Aug 7 2012
Event	Chinese National Conference on Fractal Theory and Dynamical Systems - Duration: Aug 7 2012 → …

Conference

Conference	Chinese National Conference on Fractal Theory and Dynamical Systems
Period	08/7/12 → …

Keywords

Conformal contractions
Hausdorff dimension
Infinite iterated function
Overlaps
Separation conditions
Topological pressure functions

DC Disciplines

Mathematics
Physical Sciences and Mathematics

Cite this

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title = "Infinite Iterated Function Systems With Overlaps",

abstract = " We extend the weak separation condition to in&filig;nite iterated function systems of conformal contractions with overlaps. It turns out that there are two natural but di&fflig;erent extensions. We study the topological pressure functions associated with these separation conditions. We prove a dimension formula for the Hausdor&fflig; dimension of the limit sets under the bounded distortion property and these weak separation conditions. This is joint work with Ji-Xi Tong.",

keywords = "Conformal contractions, Hausdorff dimension, Infinite iterated function, Overlaps, Separation conditions, Topological pressure functions",

author = "Sze-Man Ngai",

year = "2012",

month = aug,

day = "7",

language = "American English",

note = "Chinese National Conference on Fractal Theory and Dynamical Systems ; Conference date: 07-08-2012",

}

TY - CONF

T1 - Infinite Iterated Function Systems With Overlaps

AU - Ngai, Sze-Man

PY - 2012/8/7

Y1 - 2012/8/7

N2 - We extend the weak separation condition to in&filig;nite iterated function systems of conformal contractions with overlaps. It turns out that there are two natural but di&fflig;erent extensions. We study the topological pressure functions associated with these separation conditions. We prove a dimension formula for the Hausdor&fflig; dimension of the limit sets under the bounded distortion property and these weak separation conditions. This is joint work with Ji-Xi Tong.

AB - We extend the weak separation condition to in&filig;nite iterated function systems of conformal contractions with overlaps. It turns out that there are two natural but di&fflig;erent extensions. We study the topological pressure functions associated with these separation conditions. We prove a dimension formula for the Hausdor&fflig; dimension of the limit sets under the bounded distortion property and these weak separation conditions. This is joint work with Ji-Xi Tong.

KW - Conformal contractions

KW - Hausdorff dimension

KW - Infinite iterated function

KW - Overlaps

KW - Separation conditions

KW - Topological pressure functions

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/9

M3 - Presentation

T2 - Chinese National Conference on Fractal Theory and Dynamical Systems

Y2 - 7 August 2012

ER -

Infinite Iterated Function Systems With Overlaps

Abstract

Conference

Keywords

DC Disciplines

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