# Box dimensions of $(\times m, \times n)$ invariant sets

Date. February 12, 14h00m (UTC/GMT)

Speaker.  Natalia JURGA (University of St. Andrews)

Title. Box dimensions of $(\times m, \times n)$ invariant sets

Abstract.

We study the box dimensions of sets which are invariant under the toral endormorphism $(x, y) \mapsto (m x \mod 1, n y mod 1)$ for integers $n>m \geq 2$. This is a fundamental example of an expanding, nonconformal dynamical system, and invariant sets have many subtle properties. The basic examples of such invariant sets are Bedford-McMullen carpets and, more generally, invariant sets are modelled by subshifts on the associated symbolic space. When this subshift is topologically mixing and sofic, the situation is well-understood by results of Kenyon and Peres, in particular the box dimension satisfies a natural formula in terms of entropy and the expansion coefficients $m,n$.  In this talk we will discuss what happens beyond the sofic and mixing case, which is partly based on joint work with Jonathan Fraser (St Andrews).

Online Zoom meeting (Session will open some minutes before 14h00)
https://videoconf-colibri.zoom.us/j/81434789474?pwd=d0srRThmUlRLbzRWU1dhRnZjWXZsdz09

Meeting ID:  814 3478 9474

Start Date
Venue
Online seminar

Natalia JURGA

## Speaker's Institution

University of St. Andrews

## Area

Dynamical Systems