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Non-algebraic attractors on $\mathbf{P}^k$

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  • We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic non-algebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we construct invariant hyperbolic measures supported on the attractors with nice dynamical properties.
    Mathematics Subject Classification: Primary 32H50; Secondary 37C70.


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