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Thursday 13 Feb 2020Dynamics Seminar: Conjugacy classes of real-analytic mappings of the interval

Trevor C. Clark - Imperial College London

Building:One Constantine Leventis Teaching Room 13:30-14:30

Avila-Lyubich-de Melo proved that the topological conjugacy classes of unimodal real-analytic maps are complex analytic codimension-1 manifolds, which laminate a neighbourhood of any such mapping without a neutral cycle. I will show how to construct a "truncated polynomial-like mapping" associated to a real mapping. This gives a new complex extension of a real-analytic mapping. The additional structure provided by this extension makes it possible to generalize this result of Avila-Lyubich-de Melo to higher degree mappings. This is joint work with Sebastian van Strien.

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