Ergodic Theory and Dynamical Systems



Julia sets of expanding polymodials


ALEXANDER BLOKH a1, CHRIS CLEVELAND a2 and MICHAL MISIUREWICZ a2
a1 Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, AL 35294-2060, USA (e-mail: ablokh@math.uab.edu)
a2 Department of Mathematical Sciences, IUPUI, 402 North Blackford Street, Indianapolis, IN 46202-3216, USA (e-mail: cclevel@math.iupui.edu, mmisiure@math.iupui.edu)

Article author query
blokh a   [Google Scholar] 
cleveland c   [Google Scholar] 
misiurewicz m   [Google Scholar] 
 

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.

(Received July 2 2003)
(Revised March 28 2004)