Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial
Geometric Topology
2015-05-07 v2 Complex Variables
Dynamical Systems
Group Theory
Abstract
We study the action of the group of polynomial automorphisms of C^n (n>2) which preserve the Markoff-Hurwitz polynomial H(x):= x_1^2 + x_2^2 + ... + x_n^2 - x_1 x_2 ... x_n. Our main results include the determination of the group, the description of a non-empty open subset of C^n on which the group acts properly discontinuously (domain of discontinuity), and identities for the orbit of points in the domain of discontinuity.
Keywords
Cite
@article{arxiv.1501.06955,
title = {Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial},
author = {Hengnan Hu and Ser Peow Tan and Ying Zhang},
journal= {arXiv preprint arXiv:1501.06955},
year = {2015}
}
Comments
dedicatory added, grant support acknowledged, minor corrections, references updated