Mathematical Sciences: Dynamics of Polynomial Diffeomorphisms

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John Smillie will carry out research into the dynamics of polynomial diffeomorphisms. This research belongs to the study of chaos. Smillie will study the Henon family of transformations. These are two dimensional diffeomorphisms of importance because of the fractal nature of their invariant sets. Smillie will study the topological, differential and measure theoretic invariants of these maps. The questions will involve entropy, criteria for hyperbolicity, invariant measures and Lyapunov exponents.