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Functional equations in branched covering maps
Abstract
We study the functional equation $ f \circ p = g \circ q,$ where $ f,$ g, p, q are branched covering maps between closed surfaces. In particular, we extend results on semiconjugate holomorphic maps between compact Riemann surfaces to this broader setting. As an application, we present an alternative proof of the fact that every quotient of a torus endomorphism has a parabolic orbifold, along with some extensions of this result.
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BibTeX
@misc{pakovich2026functional,
title = {{Functional equations in branched covering maps}},
author = {Fedor Pakovich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23613},
eprint = {2609.23613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23613},
}
RIS
TY - UNPB
TI - Functional equations in branched covering maps
AU - Fedor Pakovich
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23613
UR - https://arxiv.org/abs/2609.23613
AB - We study the functional equation $ f \circ p = g \circ q,$ where $ f,$ g, p, q are branched covering maps between closed surfaces. In particular, we extend results on semiconjugate holomorphic maps between compact Riemann surfaces to this broader setting. As an application, we present an alternative proof of the fact that every quotient of a torus endomorphism has a parabolic orbifold, along with some extensions of this result.
ER -