Polynomial automorphisms of Cⁿ preserving the Markoff-Hurwitz polynomial

2015/01/27 by Hu, Hengnan, Tan, Ser Peow, Zhang, Ying
#30F60 #32G15 #37F10 #57M50 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1501.06955

Abstract

We study the action of the group of polynomial automorphisms of Cⁿ (n>2) which preserve the Markoff-Hurwitz polynomial H(x):= x₁² + x₂² + ... + x_n² - x₁ x₂ ... x_n. Our main results include the determination of the group, the description of a non-empty open subset of Cⁿ on which the group acts properly discontinuously (domain of discontinuity), and identities for the orbit of points in the domain of discontinuity.

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