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Author Fennicae, Scientiarum ♦ Hinkkanen, A.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Quasiregular Semigroups ♦ Ffi Ffi Gamma1 ♦ Rational Function ♦ Semigroup Operation ♦ Meromorphic Function ♦ Quadratic Polynomial ♦ Similar Positive Conjugacy Result ♦ Quasimeromorphic Function ♦ Open Set ♦ Quasiconformal Homeomorphism ♦ Abelian Semigroups ♦ Quasiconformal Homeomorphisms ♦ Algebraic Condition
Abstract . Let G be a semigroup of K -quasiregular or K -quasimeromorphic functions mapping a given open set U in the Riemann sphere into itself, for a fixed K , the semigroup operation being the composition of functions. We prove that if G satisfies an algebraic condition, which is true for all abelian semigroups, then there exists a K -quasiconformal homeomorphism of U onto an open set V such that all the functions in f ffi G ffi f \Gamma1 are meromorphic functions of V into itself. In particular, if U is the whole sphere then the elements of f ffi G ffi f \Gamma1 are rational functions. We give an example of a semigroup generated by two functions on the sphere, each quasiconformally conjugate to a quadratic polynomial, that cannot be quasiconformally conjugated to a semigroup of rational functions. We give another such example of a semigroup of K -quasiconformal homeomorphisms. These results extend and complement a similar positive conjugacy result of Tukia and of Sullivan for groups of ...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 1996-01-01