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Commuting pairs of endomorphisms of $\mathbb{P}^{2}$

Published online by Cambridge University Press:  19 September 2016

LUCAS KAUFMANN
LUCAS KAUFMANN*
Affiliation:
Sorbonne Universités, UPMC Université – Paris 6, IMJ-PRG, UMR 7586 CNRS, 4 place Jussieu, F-75005, Paris, France email lucas.kaufmann@imj-prg.fr
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Abstract

We consider commuting pairs of holomorphic endomorphisms of $\mathbb{P}^{2}$ with disjoint sequence of iterates. The case that has not been completely studied is when their degrees coincide after some number of iterations. We show in this case that they are either commuting Lattès maps or commuting homogeneous polynomial maps of $\mathbb{C}^{2}$ inducing a Lattès map on the line at infinity.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 3 , May 2018 , pp. 1025 - 1047
Copyright
© Cambridge University Press, 2016 

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