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Combinatorics of distance doubling maps

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Keller K., Winter S.

Fundamenta Mathematicae

2005

tom 187

nr 1

1-35

We study the combinatorics of distance doubling maps on the circle ℝ/ℤ with prototypes h(β) = 2β mod 1 and h̅(β) = -2β mod 1, representing the orientation preserving and orientation reversing case, respectively. In particular, we identify parts of the circle where the iterates $f^{∘n}$ 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 h̅ they suggest some analogies to the structure of the tricorn, the "antiholomorphic Mandelbrot set".

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Keller K.

1 Winter S.

1 2005

Wyniki wyszukiwania

Combinatorics of distance doubling maps