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Homeomorphisms from Julia sets into connectedness loci

Published online by Cambridge University Press:  03 July 2006

HIROYUKI INOU
HIROYUKI INOU
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (e-mail: inou@math.kyoto-u.ac.jp)
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Abstract

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We construct a homeomorphism from the filled Julia set of a given polynomial into the connectedness locus of the family of all polynomials of higher degree by using intertwining surgery. A polynomial in the image of such a homeomorphism has a renormalization of ‘capture’ type and the inverse map is given by the ‘marking’ of the captured critical orbit.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 4 , August 2006 , pp. 1087 - 1113
Copyright
2006 Cambridge University Press