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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract: While studying the dynamics of polynomial automorphisms in $$\mathbb{C}^2$$, it turns out that the class of Henon maps, which exhibits  extremely rich dynamical behaviour, is the single most important class to study. An extensive research has been done in this direction by many authors over the past thirty years.  In this talk, we shall see a 'rigidity' property' of Henon maps which essentially replicates a classical rigidity theorem of Julia sets for polynomial maps in the complex plane. In particular, we shall give an explicit description of the automorphisms in $$\mathbb{C}^2$$ which preserve the Julia sets  of a given Henon map.