Commuting pairs of endomorphisms of
release_izz523akuvfrxmhl2xhh4azyay
by
LUCAS KAUFMANN
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.
In application/xml+jats
format
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