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Julia sets of expanding polymodials

Published online by Cambridge University Press:  16 November 2005

ALEXANDER BLOKH ,
CHRIS CLEVELAND  and
MICHAŁ MISIUREWICZ
ALEXANDER BLOKH
Affiliation:
Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, AL 35294-2060, USA (e-mail: [email protected])
CHRIS CLEVELAND
Affiliation:
Department of Mathematical Sciences, IUPUI, 402 North Blackford Street, Indianapolis, IN 46202-3216, USA (e-mail: [email protected], [email protected])
MICHAŁ MISIUREWICZ
Affiliation:
Department of Mathematical Sciences, IUPUI, 402 North Blackford Street, Indianapolis, IN 46202-3216, USA (e-mail: [email protected], [email protected])
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Abstract

We continue studying branched covering maps of the plane with expanding properties, which we call expanding polymodials. They are analogous to piecewise expanding interval maps and have properties similar to those of complex polynomials (in particular, the Julia set and a lot of other notions from complex dynamics can be defined for expanding polymodials). In this paper we include the case when the Julia set is disconnected, study its topological properties and its Hausdorff dimension.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1691 - 1718
Copyright
2005 Cambridge University Press

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