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 - Dec 11 2012
Event	International Conference on Advances in Fractals and Related Topics - Duration: Dec 11 2012 → …

Conference

Conference	International Conference on Advances in Fractals and Related Topics
Period	12/11/12 → …

Keywords

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

DC Disciplines

Mathematics
Physical Sciences and Mathematics

Access to Document

https://www.math.cuhk.edu.hk/conference/afrt2012/AFRT-abstract-v.1.pdf

Cite this

@conference{bdb3792a9933483cab0f3d1788cc6bdf,

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 = dec,

day = "11",

language = "American English",

note = "International Conference on Advances in Fractals and Related Topics ; Conference date: 11-12-2012",

}

TY - CONF

T1 - Infinite Iterated Function Systems With Overlaps

AU - Ngai, Sze-Man

PY - 2012/12/11

Y1 - 2012/12/11

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/8

UR - https://www.math.cuhk.edu.hk/conference/afrt2012/AFRT-abstract-v.1.pdf

M3 - Presentation

T2 - International Conference on Advances in Fractals and Related Topics

Y2 - 11 December 2012

ER -

Infinite Iterated Function Systems With Overlaps

Abstract

Conference

Keywords

DC Disciplines

Access to Document

Other files and links

Fingerprint

Cite this