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Talks

Abstract: The homotopy shadowing framework of Ishii-Smillie allows us to construct conjugacies between dynamical systems which are not ‘close’ in the sense of structural stability. We do this by considering more general multivalued dynamical systems. Complex Hénon maps are polynomial diffeomorphisms of $\mathbb{C}^2$ and a result of Friedland and Milnor tells us that these maps are interesting to study in terms of the dynamics. We will present an alternative proof, in the homotopy shadowing framework of Ishii-Smillie, of the well known theorem that for Hénon maps $H_{p,a}$ which are small perturbations of hyperbolic polynomials $p$, the topology of the Julia set of $p$ determines the Julia set of $H_{p,a}$