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Une description combinatoire de l’involution définie par M sur les rationnels à dénominateur impair. (A combinatorial description of the involution defined by M on the rationals with odd denominator). (French) Zbl 0663.58018

The external rays of the Mandelbrot set with an argument rational with an odd denominator converge and associate pairwise, so defining an involution over these rationals (modulo \({\mathbb{Z}})\). We prove here the validity of a plain algorithm, proposed in [A. Douady, Sémin. Bourbaki, 35e année, Vol. 1980/81, Exp. No.599, Astérisque 105/106, 39-63 (1983; Zbl 0532.30019), (question 6)] which allows to describe this involution.

MSC:

37B99 Topological dynamics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Citations:

Zbl 0532.30019
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