Geodesic
Hausdorff dimension of biaccessible angles for quadratic polynomials
Henk Bruin1 ; Dierk Schleicher2
1 Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 1090 Wien, Austria
2 Jacobs University Bremen Research I P.O. Box 750 561 D-28725 Bremen, Germany
Fundamenta Mathematicae, Tome 238 (2017) no. 3, pp. 201-239

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A point $c$ in the Mandelbrot set is called biaccessible if two parameter rays land at $c$. Similarly, a point $x$ in the Julia set of a polynomial $z \mapsto z^2+c$ is called biaccessible if two dynamic rays land at $x$. In both cases, we say that the external angles of these two rays are biaccessible as well. We describe a purely combinatorial characterization of biaccessible (both dynamic and parameter) angles, and use it to give detailed estimates of the Hausdorff dimension of the set of biaccessible angles.
DOI : 10.4064/fm276-6-2016
Keywords: point mandelbrot set called biaccessible parameter rays land similarly point julia set polynomial mapsto called biaccessible dynamic rays land cases say external angles these rays biaccessible describe purely combinatorial characterization biaccessible dynamic parameter angles detailed estimates hausdorff dimension set biaccessible angles

Henk Bruin 1 ; Dierk Schleicher 2

1 Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 1090 Wien, Austria
2 Jacobs University Bremen Research I P.O. Box 750 561 D-28725 Bremen, Germany 
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Henk Bruin; Dierk Schleicher. Hausdorff dimension of biaccessible angles for quadratic polynomials. Fundamenta Mathematicae, Tome 238 (2017) no. 3, pp. 201-239. doi: 10.4064/fm276-6-2016

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