Journal of Mathematics of Kyoto University

Semihyperbolic transcendental semigroups

Hartje Kriete and Hiroki Sumi

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This paper deals with semihyperbolic semigroups which are generated by entire (possibly transcendental) functions. In particular, a criterion is given assuring that a given entire semigroup is semihyperbolic. Note that a semihyperbolic semigroup $G$ admits holomorphic scaling, that is to say, the branches of local inverses of functions $f \in G$ are of bounded degree and that the preimages shrink to zero in diameter.

Article information

J. Math. Kyoto Univ., Volume 40, Number 2 (2000), 205-216.

First available in Project Euclid: 17 August 2009

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Zentralblatt MATH identifier

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 37F15: Expanding maps; hyperbolicity; structural stability 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets


Kriete, Hartje; Sumi, Hiroki. Semihyperbolic transcendental semigroups. J. Math. Kyoto Univ. 40 (2000), no. 2, 205--216. doi:10.1215/kjm/1250517712.

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