Dynamical Systems and Analysis Seminar - Phil Rippon & Gwyneth Stallard
| Dates: | 12 May 2025 |
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| Times: | 14:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Talk I.
Speaker: Gwyneth Stallard (The Open University)
Title: Wandering domains and non-autonomous dynamics
Abstract: Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, there is a fascinating array of possible types of wandering domains. New results on the relationship between the behaviour of orbits of points in the interior of wandering domains, and orbits of points on the boundary can be proved in a very general context. We show how this has led to a generalisation of results from ergodic theory concerning recurrence and shrinking targets to the setting of boundary dynamics for non-autonomous systems of holomorphic maps.
Talk II.
Speaker: Phil Rippon (The Open University)
Title: On forward compositions of inner functions
Abstract: In a recent paper we gave sharp results about the recurrent behaviour on the boundary of the unit disc of forward compositions of inner functions, inspired by well known results on the iteration of individual inner functions. In this talk, we discuss an alternative approach to these problems, by generalising results of Pommerenke on such forward compositions of inner functions.
The talks are based on joint work of the speakers with Anna Miriam Benini, Vasiliki Evdoridou and Nuria Fagella
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
