OU Dynamical Systems seminar

The Dynamical Systems group at the Open University is organising an online seminar series.  

Our group's interests include -but are not restricted to:  Aperiodic Order,  Computer-assisted proofs in dynamical systems,  Energy systems modelling,  Holomorphic Dynamics,  Hyperbolic Geometry and Cocycle Dynamics,  Renormalisation in dynamical systems and its applications,  Symbolic Dynamics,  Tiling Dynamical Systems,  and Topological Dynamics.

Upcoming seminars

• Wednesday 14 January 2.00pm

Speaker: Julia Münch, University of Liverpool

Title: Extensions and applications to Sullivan's dictionary 

Abstract: For generalising complex dynamics to higher real dimensions it is natural to consider quasi-regular mappings. The subfamily of uniformly quasi-regular mappings is particularly well understood but it is difficult to find interesting examples. I will be talking about a result obtained joint with Daniel Meyer; we showed that one can extend a certain class of holomorphic functions (expanding Thurston maps) on the Riemann sphere S^2 to a uniformly quasi-regular mapping F defined on a subset Ω of R^3 containing S^2 in its interior.

In the second part of the talk we will present two applications of this construction that is motivated by Sullivan’s dictionary. Sullivan’s dictionary stipulates an analogy between objects, conjectures and theorems in complex dynamics and the study of Kleinian groups. The aim of the talk is to explain a construction of a space-filling curve that is the boundary of an immersed and severely folded plane. A second object will be a natural nice embedding of the hyperbolic plane that traces out a curve arising dynamically from f.

Past seminars and seminar schedule