Attracting Currents and Equilibrium Measures for Quasi-attractors of \mathbb P^k

2016/09/02 by Johan Taflin, Taflin, Johan
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Chaos control and synchronization

paper · pdf · doi:10.48550/arxiv.1609.00605

Abstract

Let f be a holomorphic endomorphism of \mathbb P^k of degree d. For each quasi-attractor of f we construct a finite set of currents with attractive behaviors. To every such an attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of \mathbb P^k. As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of log d. We also show that the study of these analytic objects can initiate a bifurcation theory for attracting sets.

Citations

• Etude des mesures hyperboliques pour les applications meromorphes

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