# Foundations of Dynamical Systems Theory

Another research area within our centre are rigorous mathematical aspects of dynamical systems. Our core expertise in this area includes ergodic theory, transfer operators and their spectra, topological dynamics, generalised shift maps, optimization problems in dynamical systems, algebraic invariants of symbolic dynamical systems, and a variety of specialized topics at the frontline of current research in dynamical systems and ergodic theory. Staff members who mainly work in this area include (in alphabetic order) Oscar Bandtlow, Alex Clark, Oliver Jenkinson, Ian Morris, Reem Yassawi. Some of our research is concerned with applications of dynamical systems theory to other areas of mathematics and physics. This includes self-affine structures in fractal geometry, multifractals, the thermodynamic formalism, joint spectral characteristics of sets of matrices, the analysis of number-theoretic algorithms, the metric geometry of measurable subsets of the plane, substitutional and tiling systems in aperiodic order, and much more.

A deformed Penrose tiling (work by A. Clark et al.)

Strongly irreducible self-affine fractal whose Hausdorff dimension is precisely known (work by I. Morris et al. in Trans. Am. Math. Soc. 2019)