Dynamical Systems and Analysis Seminar - Peej Ingarfield
| Dates: | 13 October 2025 |
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| Times: | 14:00 - 14:00 |
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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: Peej Ingarfield (University of Manchester)
Title: Dimension drop and estimating the gap
Abstract: Iterated function systems (IFS) have played a key role in the study of fractals. When considering an IFS, studying what separation properties it has gives a great amount of information about the fractal associated to the IFS. In the case that the IFS satisfies the open set condition then Hutchinsons formula gives an exact form for the Hausdorff dimension of the fractal.
This leads to the natural question of what can we say about Hausdorff dimension when an IFS fails to meet the open set condition or even has overlaps. In this talk we will discuss exact overlaps and how they are conjectured to be the cause of a phenomenon called dimension drop. After this context has been established we shall compare methods to estimate the amount this dimension can drop for a class of self similar measures with overlaps.
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
