Combinatorics of distance doubling maps

Karsten Keller*, Steifen Winter

*Corresponding author for this work


We study the combinatorics of distance doubling maps on the circle ℝ/ℤ with prototypes h(β) = 2β mod 1 and h̄(β) = -2β mod 1, representing the orientation preserving and orientation reversing case, respectively. In particular, we identify parts of the circle where the iterates fon of a distance doubling map f exhibit "distance doubling behavior". The results include well known statements for h related to the structure of the Mandelbrot set M. For h̄ they suggest some analogies to the structure of the tricorn, the " antiholomorphic Mandelbrot set".

Original languageEnglish
JournalFundamenta Mathematicae
Issue number1
Pages (from-to)1-35
Number of pages35
Publication statusPublished - 01.01.2005


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