Commuting pairs of endomorphisms of P^2
Complex Variables
2016-09-28 v1 Dynamical Systems
Abstract
We consider commuting pairs of holomorphic endomorphisms of P^2 with disjoint sequence of iterates. The remaining case to be studied is when their degrees coincide after some number of iterations. We show in this case that they are either commuting Latt\`es maps or commuting homogeneous polynomial maps of C^2 inducing a Latt\`es map on the hyperplane at infinity.
Keywords
Cite
@article{arxiv.1509.06534,
title = {Commuting pairs of endomorphisms of P^2},
author = {Lucas Kaufmann},
journal= {arXiv preprint arXiv:1509.06534},
year = {2016}
}
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22 pages