Combinatorics of distance doubling maps

• Autorzy: Karsten Keller , Steffen Winter
• Języki publikacji: EN

Abstrakty

EN

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".

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37E10: Maps of the circle
• 37F20: Combinatorics and topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 187
• Numer: 1
• Strony: 1-35

Daty

wydano

2005

Twórcy

autor

Karsten Keller

• Mathematical Institute, University of Lübeck, Wallstr. 40, D-23560 Lübeck, Germany

autor

Steffen Winter

• Mathematical Institute, University of Jena, D-07740 Jena, Germany

Identyfikatory

DOI

10.4064/fm187-1-1