The class of Henon maps is the most important class of polynomial automorphisms in the two dimensional complex space C^2. These are where the modern breakthrough in complex dynamics happened and till date it remained a central theme of study in multi-variable holomorphic dynamics. The present proposal deals with some significant properties of Henon maps which are expected to determine the underlying Henon maps almost uniquely. These properties are called 'rigidity' properties of Henon maps. The questions I discussed in the present proposal are inspired by the classical rigidity results for polynomial maps in one dimensional complex plane.
Indian Institute of Science
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