Combinatorics of distance doubling maps

Karsten Keller, and Steffen Winter. "Combinatorics of distance doubling maps." Fundamenta Mathematicae 187.1 (2005): 1-35. <http://eudml.org/doc/282709>.

@article{KarstenKeller2005,
abstract = {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”.},
author = {Karsten Keller, Steffen Winter},
journal = {Fundamenta Mathematicae},
keywords = {combinatorial structure; orientation-preserving map; orientation-reversing map; iteration; chords; breading sequences; bifurcation; maps on the circle; distance doubling behavior; Mandelbrot set; tricorn},
language = {eng},
number = {1},
pages = {1-35},
title = {Combinatorics of distance doubling maps},
url = {http://eudml.org/doc/282709},
volume = {187},
year = {2005},
}

TY - JOUR
AU - Karsten Keller
AU - Steffen Winter
TI - Combinatorics of distance doubling maps
JO - Fundamenta Mathematicae
PY - 2005
VL - 187
IS - 1
SP - 1
EP - 35
AB - 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”.
LA - eng
KW - combinatorial structure; orientation-preserving map; orientation-reversing map; iteration; chords; breading sequences; bifurcation; maps on the circle; distance doubling behavior; Mandelbrot set; tricorn
UR - http://eudml.org/doc/282709
ER -