On chain recurrence classes of endomorphisms of $\mathbb {P}^k$

Johan Taflin (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We prove that the minimal chain recurrence classes of a holomorphic endomorphism of Pkhave finitely many connected components. We also obtain results on arbitrary classes. These strong constraints on the topological dynamics in the phase space are all deduced from the associated action on a space of currents.

Mots clés: Chain recurrent set; attractors

Domaines: Mathématiques [math]

Johan Taflin. On chain recurrence classes of endomorphisms of $\mathbb {P}^k$. Proceedings of the American Mathematical Society, 2022, ⟨10.1090/proc/15947⟩. ⟨hal-03552972⟩