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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

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Events for 25 June 2020

Pablo Guarino: Quasisymmetric orbit-flexibility

1:00pm, The talk will be broadcast via Zoom.

In this talk we will discuss the following dynamical notion: two given orbits of a minimal circle homeomorphism f are said to be geometrically equivalent if there exists a quasisymmetric circle homeomorphism identifying both orbits and commuting with f. By a well-known theorem due to Herman and Yoccoz, if f is a smooth diffeomorphism with Diophantine rotation number, then any two orbits are geometrically equivalent. As it follows from the a-priori bounds of Herman and Swiatek, the same holds if f is a critical circle map with rotation number of bounded type. By contrast, in collaboration with Edson de Faria (Universidade de São Paulo), we recently proved that if f is a critical circle map whose rotation number belongs to a certain full Lebesgue measure set in (0,1), then the number of equivalence classes is uncountable. The proof of this result relies on the ergodicity of a two-dimensional skew product over the Gauss map. If there is enough time, we will show how, as a by-product of our techniques, we were able to construct topological conjugacies between multicritical circle maps which are not quasisymmetric, and how we show that this phenomenon is abundant, both from the topological and measure-theoretical viewpoints.

Contact mark.a.powell@durham.ac.uk, andrew.lobb@durham.ac.uk, wilhelm.klingenberg@durham.ac.uk, fernando.galaz-garcia@durham.ac.uk for more information about this event.