CORDIS Project
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This project explores the fractal geometry of invariant sets in compact abelian groups, focusing on conjectures related to dynamics and equidistribution. It combines techniques from various mathematical fields to address these complex problems.
We propose to study the fractal geometry of invariant sets for endomorphisms of compact abelian groups, specifically a family of conjectures by Furstenberg on the dimensions of orbit closures under such dynamics, and on the size of sums and intersections of invariant sets.
These conjectures are related to problems on expansion in integer bases, in Diophantine approximation, measure rigidity, analysis and equidistribution.
The project focuses on the conjectures themselves and some related problem…
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