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Carrots for dessert

Published online by Cambridge University Press:  17 November 2011

CARSTEN LUNDE PETERSEN  and
PASCALE ROESCH
CARSTEN LUNDE PETERSEN
Affiliation:
IMFUFA, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark (email: [email protected])
PASCALE ROESCH
Affiliation:
Institut de Mathématiques de Toulouse, Université Paul Sabatier, F-31062 Toulouse Cedex 9, France (email: [email protected])
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Abstract

We formulate and prove a precise statement of asymptotic shrinking of ‘carrot-fields’ around the Mandelbrot set M. This phenomenon was suggested in a seminal text on polynomial-like mappings by Douady and Hubbard [On the dynamics of polynomial-like mappings. Ann. Sci. Éc. Norm. Supér. t.18 (1985), 287–343]. This is helpful for understanding how copies of M sit in the bifurcation loci of families of rational maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 6 , December 2012 , pp. 2025 - 2055
Copyright
Copyright © Cambridge University Press 2011

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