In general, a dynamical system can be thought of as a semigroup acting on a set. I study topological dynamical systems, where the space is a compact metric space and the semigroup is generated by a single continuous, usually non-invertible, map. I am especially interested in how the topology of the space constrains or enables different kinds of asymptotic behaviour.

Many spaces that arise in dynamics, for example as attractors or inverse limits, are continua whose local structure is far more complicated than that of a manifold. I study how this structure shapes the dynamics: which properties a map on such a space can or must have. Two projects that fit this theme best are the study of tranched graphs (with Piotr Oprocha) and the proof that every nondegenerate Peano continuum admits a pure mixing selfmap (with Klára Karásová and Piotr Oprocha).

Going forward, I want to keep exploring this interplay in both directions: how the structure of a space restricts the maps it supports, and which continua arise from dynamics itself, for example as inverse limits or as attractors. I am also interested in how far topological and dynamical invariants determine a system up to conjugacy. Beyond single maps, I would like to study more general semigroup actions.

Details, abstracts and links for all papers are on the Papers page.