Polynomial automorphisms of Cn preserving the Markoff-Hurwitz polynomial
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 + ... + xn2 - x1 x2 ... xn. 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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