Commuting pairs of endomorphisms of release_izz523akuvfrxmhl2xhh4azyay

by LUCAS KAUFMANN

Published in Ergodic Theory and Dynamical Systems by Cambridge University Press (CUP).

2016   Volume 38, Issue 03, p1025-1047

Abstract

We consider commuting pairs of holomorphic endomorphisms of <jats:inline-formula> <jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0143385716000547_inline3" xlink:type="simple" /><jats:tex-math>$\mathbb{P}^{2}$</jats:tex-math></jats:alternatives> </jats:inline-formula> 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 <jats:inline-formula> <jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0143385716000547_inline4" xlink:type="simple" /><jats:tex-math>$\mathbb{C}^{2}$</jats:tex-math></jats:alternatives> </jats:inline-formula> inducing a Lattès map on the line at infinity.
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Type  article-journal
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Date   2016-09-19
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