Topology and Dynamics 

3D image of a gasket

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
  • C*-dynamical systems
  • Chaos and deterministic behaviour
  • Induced dynamical systems
  • Jarník and Besicovitch (type) sets
  • Low dimensional dynamical systems and their complexity
  • Shadowing properties
  • Symbolic dynamics
  • Tilings and quasicrystals

In addition to this we also work on questions in set-theoretic and general topology, logic and complex systems theory.

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

Professor Chris Good

Professor of Mathematics

Chris Good is Professor of Mathematics at the University of Birmingham. He is the author of over 50 research articles in general topology, set-theoretic topology, topological dynamics and mathematical education.  He regularly collaborates with mathematicians around the world, including colleagues from Mexico, New Zealand, Poland and the US, as well as from Oxford, and has organised conferences in Birmingham, Oxford and Cambridge. 

Profile

Dr Simon Baker

Lecturer

Simon Baker is a lecturer in the School of Mathematics. He is interested in topics from ergodic theory, fractal geometry, and number theory. Specific areas include beta expansions, Diophantine approximation, and iterated function systems. He regularly gives invited talks at events held in the UK and abroad.

Profile

Dr Sabrina Kombrink

Lecturer

Sabrina Kombrink is a lecturer of Mathematics. She 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 interim of analysis, geometry and stochastics.

Profile

Dr Robert Leek

Lecturer

Robert Leek is lecturer of Mathematics at the University of Birmingham.

Dr Tony Samuel

Lecturer

Tony is a Lecturer (Assistant Professor) of Mathematics and Statistics at the University of Birmingham. He has held academic posts at California Polytechnic State University, Universität Bremen, Australian National University and the University of St Andrews. He has also had the privilege of holding prolonged research stays at the Hausdorff Research Institute for Mathematics, Humboldt–Universität zu Berlin, Institut Mittag–Leffler, and South China University of Technology.

Since 2020 he has been a Fellow of the Higher Education Academy, and the Director of Student Experience for J-BJI – a joint institute which runs a transnational undergraduate education programme. Further, in 2018 he was honoured with the Terrance Harris Excellence in Mentorship Award from California Polytechnic State University.

Tony's research interests are in aperiodic order, Diophantine approximations, dynamical systems, and potential theory. For links to pre-prints of his research articles, as well as his peer reviewed publications, please visit arXiv and Google Scholar. Now and then, he also write reviews for MathSciNet and zbMATH.

For further details on lecture courses Tony has taught, research projects and dissertations he has supervised, and articles he has published please visit Tony’s University of Birmingham Profile.  Alternatively, please visit his Mathematics homepage.

Postdocs


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

PhD Students

Current PhD Students

Previous PhD Students

  • Joel Mitchell (2021)
  • Dolores Columba Perez Flores (2017)
  • Mate Puljiz (2017)
  • Kyriakos Papadopoulos (2012)
  • Amna Ahmed (2012)
  • Che Dzul-Kifli (2012)
  • Andrew Barwell (2010)
  • Lylah Haynes (2006)