Topology and Dynamics

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The mathematical theory of dynamical systems is a vital part of modern mathematical analysis, where new theoretical developments have been inspired by applications in physics and nature. Thus, this theory forms a strong bridge between pure and applied mathematics as well as many other areas of the natural sciences.

Our research focuses mainly on studying topological and ergodic aspects of dynamical systems and their interactions with problems occurring within algebra, combinatorics, geometry, number theory and physics.

The fundamental research theme is to study (continuous) functions mapping (compact) topological spaces to themselves. As the function is iterated (repeatedly applied), asymptotic structures appear for example periodic orbits, recurrent and non-wandering points, as well as minimal sets.

Results from ergodic theory can be used to develop a understanding of such structures, points and sets, by taking a probabilistic viewpoint to investigate the average statistical behaviour of the system. Here, the central objects of study are measures, this leads to the question which ones are important, and what happens for typical points for these measures under repeated application of given map? This naturally leads to applications and developments of multifractals and the thermodynamic formalism as pioneered by David Ruelle and Rufus Bowen. Taking things one step further, one can then begin to study the speed at which the system begins to look completely random, a key signature of what is nowadays known as chaotic behaviour.

Areas of active research within our group include, but are not limited to, the following.

  • The Auslander-Yorke dichotomy
  • β-transformations and interval maps
  • Bifurcation theory
  • Chaos and deterministic behaviour
  • Fractal geometry
  • Induced dynamical systems
  • Jarník and Besicovitch (type) sets
  • Low dimensional dynamical systems and their complexity
  • Shadowing properties
  • Symbolic dynamics
  • Tilings and quasicrystals
  • Thermodynamic formalism

We welcome enquiries from potential research students, postdocs and visitors who wish to work within our group. Specific research interests of the members of the group are given below.

Head of Topology Group

Dr Tony Samuel

Associate Professor of Mathematics
Head of Topology and Dynamics
Director of Student Experience (J-BJI)

Tony's mathematical research interests lie in aperiodic order (mathematical quasicrystals), Diophantine approximations, dynamical systems, fractal geometry, and numeration systems. More recently he has become interested in developing interactive educational materials using RStudio and the Python library Manim.

Academic Staff

Professor Chris Good

Professor Chris Good

Head of School
Professor of Mathematics

Professor Good's research considers: characterisations of maps with the shadowing property; dynamical systems with a topological rather than metric phase space; the Auslander-Yorke dichotomy, equicontinuity, transitivity and sensitivity; countable dynamical systems; induced dynamics on hyperspaces and function spaces; coarse graining of complex systems.

Dr Sabrina Kombrink

Dr Sabrina Kombrink

Assistant Professor of Mathematics
Senior Tutor (J-BJI)

Sabrina is interested in geometrically characterising highly irregular objects as well as in the question which geometric features one can hear when listening to the sound of a fractal drum. Her research lies in the intersection of analysis, geometry and stochastics.

Dr Robert Leek

Assistant Professor of Mathematics
Director for Computer-Aided Assessment
Examinations Officer

Dr Robert Leek is an Assistant Professor at the University of Birmingham, where he is also the Director for Computer-Aided Assessment and the Examinations Officer.  His research interests revolve around topology, and in more recent years topological dynamics.

PhD Students

Note that not all PhD researchers have requested profiles.

Previous Research Fellows

  • Alessandro Pezzoni (2020-2021)
  • Dan Rust (2019-2020)
  • Jonathan Meddaugh (2015-2017)
  • Leobardo Fernandez Roman (2013-2016)
  • Ziqin Feng (2012-2013)