Dynamical Systems and Analysis Seminar - Paul Glendinning
| Dates: | 20 October 2025 |
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| Times: | 14:00 - 15:00 |
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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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Speaker: Paul Glendinning (University of Manchester)
Title: The boundary of chaos and the boundary of positive Hausdorff dimension of survivor sets for two-branch maps of the interval
Abstract: Two classical problems in bifurcation theory are the characterisation of the boundary of chaos (in the sense of positive topological entropy) of families of maps, and the boundary of positive Hausdorff dimension of survivor sets in open maps (maps with 'holes' in phase space, the survivor set is the set of points whose forward iterates never land in the hole). In one dimension these two problems are effectively equivalent, and I will give a complete description of the boundary for classes of expanding maps with two monotonic branches and either a hole or a plateau. There is a natural two-parameter family associated with these maps (the position of the hole/plateau) and I will show that there are two classes of codimension one transitions for these maps (and uncountably many codimension two points!). Much of this work is joint with Clement Hege.
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
