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Self-affine Systems and Hausdorff Dimension Theory - Lecture 1B

Simons Semester on Dynamics via YouTube

Overview

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Explore the dimension theory of self-affine systems in this 44-minute lecture from the Simons Semester on Dynamics series. Delve into the complexities of calculating Hausdorff dimensions for planar self-affine sets, focusing on cases involving strong separation of cylinders and strong irreducibility of linear parts. Learn how the well-understood principles of conformal transformations in iterated function systems (IFS) become more challenging when dealing with non-conformal maps and affine transformations. Examine fundamental results from Falconer and recent developments based on collaborative research with Antti Kaenmaki, Mike Hochman, and Ariel Rapaport.

Syllabus

Balázs Bárány (Budapest University of Technology and Economics), lecture 1b

Taught by

Simons Semester on Dynamics

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