Reading course on Dynamical Systems in Fractal Geometry

We’ll mainly follow this.

There are some books that may be helpful during the reading course, such as:

• Walters, ‘An introduction to Ergodic Theory’ (for measure entropy, topological entropy, pressure, etc)

• Falconer, ‘Techniques in Fractal Geometry’ (for cookie cutters, pressure and gibbs measures, etc)

• Falconer, ‘Fractal Geometry: Mathematical Foundations and Applications’ (for extra information of IFS and dimension)

Talks:

• Talk1 Introduction to Dynamics

• Talk2 Introduction to Fractal Geometry

• Talk3 Intro to cookie cutters

• Talk4 Cookie Cutter Set Measure 0

• Talk5 Talk5b Topological entropy

• Talk6 Measure entropy and variational principle

• (there are not notes for the Oct 30 talk on projections)

• Talk7 Topological pressure, Ruelle operator, and Gibbs measures

• Talk 8 Bowen's formula

• Talk 9 and Notes of talk 9 Markov Partitions

Schedule:

Sept 4: Organization meeting + introduction to dynamics (Brian Marcus)

Sept 18: introduction to fractal geometry (Alexia Yavicoli)

Sept 25: cookie cutters systems, IFSs, self-similarity, conjugacy between cookie-cutter and full shift (Hein)

Oct 2: bounded variation and lebesgue measure zero for C^{1+gamma} cookie cutter limit sets (Chengyu)

Oct 9: Topological Entropy and analogy with notions of dimension (Ethan)

Oct 16: Measure-theoretic Entropy and variational principle (Natalia)

Oct 30: A brief survey on the dimension of projections (Pablo Shmerkin)

Nov 6: Topological pressure, Ruelle operator, and Gibbs measures (Ignacio)

Nov 13: Bowen’s  equation for Hausdorff dimension of cookie cutters (Petr)

Nov 20: Markov Partitions. Fractal boundaries of Markov Partitions (Huub)

Nov 27: Markov Partitions. Fractal boundaries of Markov Partitions part 2 (Chayce)

Dec 4: Cookie-cutters and Horseshoes (Matt)

Participants and emails:

Brian Marcus marcus@math.ubc.ca

Alexia Yavicoli yavicoli@math.ubc.ca

Pablo Shmerkin pshmerkin@math.ubc.ca 

Ignacio Andres Rojas Aravena i.andres@math.ubc.ca

Natalia Mora Cuellar natalia.mora@math.ubc.ca

Chengyu Wu chengyuw@connect.hku.hk

Huub De Jong huub.dejong@math.ubc.ca

Petr Kosenko pkosenko@math.ubc.ca

Hein Thant Aung heinta@student.ubc.ca

Ethan Armitage arimteth@math.ubc.ca

Chayce Hughes chahug21@student.ubc.ca

Mattew BullWeizel mbullweizel@icloud.com

Kaining Jia kaining.jia@math.ubc.ca

Zhiqiang zqwang@math.ubc.ca

Ali Fele Paranj ali.fele@gmail.com