Topics in Ergodic Theory and Fractal Geometry

نظرة عامة على البرنامج

This PhD program explores invariant sets and measures in iterated function systems, combining Ergodic Theory and Fractal Geometry. It aims to understand the cardinality and complexity of codings for points in invariant sets and the number theoretic properties of typical points within them. The program's research impact is highly rated, with 94% of Loughborough's research being world-leading or internationally excellent.

مخطط البرنامج

The project lies at the intersection of Ergodic Theory and Fractal Geometry. The goal is to approach this topic from various angles, including:

• Understanding the cardinality and complexity of the set of codings for a point in the invariant set.
• Understanding the number theoretic properties of a typical point belonging to the invariant set.
This goal can be approached from various angles. Specific problems include understanding the cardinality and complexity of the set of codings for a point in the invariant set or understanding the number theoretic properties of a typical point belonging to the invariant set. This project lies at the intersection of Ergodic Theory and Fractal Geometry. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021