# Dimension of attractors for Iterated Function Systems of linear fractional transformations and the Diophantine property of matrix semigroups

Seminar
Speaker
Dr. Yuki Takahashi, Bar-Ilan University
Date
05/11/2018 - 15:15 - 14:00Add to Calendar 2018-11-05 14:00:00 2018-11-05 15:15:00 Dimension of attractors for Iterated Function Systems of linear fractional transformations and the Diophantine property of matrix semigroups We consider Iterated Function Systems of linear fractional transformations, and show that the Hausdorff dimension of the attractor is given by the Bowen's pressure formula, if the Iterated Function Systems satisfy the exponential separation condition. We also show that almost every finite collections of \$GL_n( \mathbb{R} )\$ matrices are Diophantine if the matrices have positive entries. This is a joint work with Boris Solomyak. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

We consider Iterated Function Systems of linear fractional transformations, and show that the
Hausdorff dimension of the attractor is given by the Bowen's pressure formula, if the Iterated
Function Systems satisfy the exponential separation condition. We also show that almost every
finite collections of \$GL_n( \mathbb{R} )\$ matrices are Diophantine if the matrices have positive
entries. This is a joint work with Boris Solomyak.

תאריך עדכון אחרון : 04/11/2018