#### Marco Lopez

Thursday, September 6, 2018

Manchester 020, 11:00am

### Hausdorff dimension of shrinking-target sets:

Fractal geometry and dynamical systems

The ” shrinking target problem” refers to the study of the set of points in a metric space whose orbits under a dynamical system it infinitely often a ball with radius shrinking to zero. Historically, such sets arise from Diophantine approximation and since then they have been studied in other contexts. One difficult question regarding such sets is their fractal dimension, in particular their Hausdorff dimension. In this talk we will define Hausdorff dimension and present some basic examples for certain dynamically-defined sets. We will then focus on shrinking-target sets and touch upon the theory of thermody-namic formalism, which has been used to establish a formula for the dimension of certain fractal sets.

Host: Dr. John Gemmer (gemmerj@wfu.edu)

Department of Mathematics & Statistics