External rays and the real slice of the Mandelbrot set
نویسندگان
چکیده
منابع مشابه
External Rays and the Real Slice of the Mandelbrot Set
This paper investigates the set of angles of the parameter rays which land on the real slice [−2, 1/4] of the Mandelbrot set. We prove that this set has zero length but Hausdorff dimension 1. We obtain the corresponding results for the tuned images of the real slice. Applications of these estimates in the study of critically non-recurrent real quadratics as well as biaccessible points of quadra...
متن کاملRational External Rays of the Mandelbrot Set
We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is di erent from the original one, given by Douady and Hubbard and re ned by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depende...
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We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is different from the original one, given by Douady and Hubbard and refined by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depen...
متن کاملDrawing and computing external rays in the multiple-spiral medallions of the Mandelbrot set
The multiple-spiral medallions are beautiful decorations of the Mandelbrot set. Computer graphics provide an invaluable tool to study the structure of these decorations with central symmetry, formed by an infinity of baby Mandelbrot sets that have high periods. Up to now, the external arguments of the external rays landing at the cusps of the cardioids of these baby Mandelbrot sets could not be...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2003
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385702001335