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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 thegroup, the description of a non-empty open subset of C^n on which the groupacts properly discontinuously (domain of discontinuity), and identities for theorbit of points in the domain of discontinuity.

Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial