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Combinatorics of distance doubling maps

Karsten Keller, Steffen Winter (2005)

Fundamenta Mathematicae

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 $f^{\circ n}$ 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...

Conformal measures and matings between Kleinian groups and quadratic polynomials

Marianne Freiberger (2007)

Fundamenta Mathematicae

Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ is equal to the Hausdorff dimension of the limit set. Moreover, when f is the limit of a pinching deformation ${f_{t}}_{0 \leq t < 1}$ we give sufficient conditions for the dynamical convergence of $f_{t}$ .

Contractive curves.

Bonifant, Araceli, Dabija, Marius (2002)

International Journal of Mathematics and Mathematical Sciences

Coupling patterns of external arguments in the multiple-spiral medallions of the Mandelbrot set.

Romera, M., Pastor, G., Orue, A.B., Arroyo, D., Montoya, F. (2009)

Discrete Dynamics in Nature and Society

Displaying 1 – 4 of 4

Combinatorics of distance doubling maps

Conformal measures and matings between Kleinian groups and quadratic polynomials

Contractive curves.

Coupling patterns of external arguments in the multiple-spiral medallions of the Mandelbrot set.

Currently displaying 1 – 4 of 4