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Complex dynamics of Möbius semigroups

Published online by Cambridge University Press:  07 February 2012

DAVID FRIED ,
SEBASTIAN M. MAROTTA  and
RICH STANKEWITZ
DAVID FRIED
Affiliation:
Department of Mathematics, Boston University, USA (email: [email protected])
SEBASTIAN M. MAROTTA
Affiliation:
Department of Mathematics, University of the Pacific, USA (email: [email protected])
RICH STANKEWITZ
Affiliation:
Department of Mathematical Sciences, Ball State University, USA (email: [email protected])
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Abstract

We study the dynamics of semigroups of Möbius transformations on the Riemann sphere, especially their Julia sets and attractors. This theory relates to the dynamics of rational functions, rational semigroups, and Möbius groups and we compare and contrast these theories. We particularly examine Caruso’s family of Möbius semigroups, based on a random dynamics variant of the Fibonacci sequence.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 6 , December 2012 , pp. 1889 - 1929
Copyright
Copyright © Cambridge University Press 2012

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