On chain recurrence classes of endomorphisms of $\mathbb {P}^k$
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- by Johan Taflin
- Proc. Amer. Math. Soc. 150 (2022), 3941-3951
- DOI: https://doi.org/10.1090/proc/15947
- Published electronically: April 14, 2022
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Abstract:
We prove that the minimal chain recurrence classes of a holomorphic endomorphism of $\mathbb {P}^k$ have 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.References
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Bibliographic Information
- Johan Taflin
- Affiliation: Université de Bourgogne-Franche-Comté, IMB, CNRS UMR 5584, Faculté des Sciences Mirande, 9 avenue Alain Savary, F-21000 Dijon, France
- MR Author ID: 889224
- Email: johan.taflin@u-bourgogne.fr
- Received by editor(s): May 12, 2021
- Received by editor(s) in revised form: December 7, 2021
- Published electronically: April 14, 2022
- Additional Notes: This work was supported by the ANR grant Fatou ANR-17-CE40-0002-01, the EIPHI Graduate School (contract ANR-17-EURE-0002) and Bourgogne-Franche-Comté Region.
- Communicated by: Filippo Bracci
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3941-3951
- MSC (2020): Primary 32H50, 37F10
- DOI: https://doi.org/10.1090/proc/15947
- MathSciNet review: 4446242