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On the dynamics of polynomial-like mappings
Applications de type polynomial. Familles analytiques de telles applications. Resultats negatifs. Familles a un parametre d'applications de degre 2. Petites copies de M dans M. Carrottes pour le…
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Quadratic differentials and foliations
This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the "…
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A proof of Thurston's topological characterization of rational functions
The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference in Duluth, 1983, where one of the…
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How to find all roots of complex polynomials by Newton’s method
Abstract.We investigate Newton’s method to find roots of polynomials of fixed degree d, appropriately normalized: we construct a finite set of points such that, for every root of every such…
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The iteration of cubic polynomials Part I: The global topology of parameter space
Fonctions univalentes en dynamique analytique complexe. Torsion de la structure complexe. Topologie globale de l'espace parametre
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Differential Equations: A Dynamical Systems Approach
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Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
This volume is the second of four volumes devoted to Teichmuller theory and its applications to geometry, topology, and dynamics. The first volume gave an introduction to Teichmuller theory. Volumes…
Hénon mappings in the complex domain I: The global topology of dynamical space
© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
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On the density of strebel differentials
w 1. Statement of the Main Result Let X be a compact Riemann surface of genus g > 2 and denote by O the sheaf of germs of holomorphic differential 1-forms on X. Let q~H~ ~| be a nonzero holomorphic…
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Hénon Mappings in the Complex Domain
Let H: ℂ2 → ℂ2 be the Henon mapping given by $$ \left[ {_y^x} \right] \mapsto \left[ {_x^{p(x) - ay}} \right] $$ The key invariant subsets are K ±, the sets of points with bounded forward…
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