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arXiv · 1609.00605

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

Johan Taflin
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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.

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Johan Taflin. 2016-09-02. Attracting Currents and Equilibrium Measures for Quasi-attractors of $\mathbb P^k$. https://arxiv.org/abs/1609.00605

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