We demonstrate that the question whether or not a given topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.
We give a presentation for the baseleaf preserving mapping class group MCG.H/ of the punctured solenoid H. The generators for our presentation were introduced previously, and several relations among them were derived. In addition, we show that MCG.H/ has no non-trivial central elements. Our main tool is a new complex of triangulations of the disk upon which MCG.H/ acts.
For any complex Hénon map H P, a : x y � → P(x) − ay x , the universal cover of the forward escaping set U + is biholomorphic to D × C, where D is the unit disk. The vertical foliation by copies of C descends to the escaping set itself and makes it a rather rigid object. In this note, we give evidence of this rigidity by showing that the analytic structure of the escaping set essentially characterizes the Hénon map, up to some ambiguity which increases with the degree of the polynomial P.
We consider in this paper a sequence of complex analytic functions constructed by the following procedure fn(z) = f n−1 (z)f n−2 (z) + c, where c ∈ C is a parameter. Our aim is to give a thorough dynamical study of this family, in particular we are able to extend the familiar notions of Julia sets and Green function and to analyze their properties. As a consequence, we extend some well-known results. Finally we study in detail the case where c is small.
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