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Complex dynamics and geometry. Papers from the Meeting ”State of the art of the research of the Sociéteé Mathématique de France”, Lyon, France, January 1997. (Dynamique et géométrie complexes.) (French) Zbl 1010.00008
Panoramas et Synthèses. 8. Paris: Société Mathématique de France. Providence, RI: American Mathematical Society, xii, 222 p. (1999).

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Summary: In the last twenty years, the theory of holomorphic dynamical systems has had a resurgent activity, in particular concerning the fine analysis of Julia sets associated to polynomials and rational maps in one complex variable. Simultaneously, closely related theories have had a similar rapid development, for instance, the qualitative theory of differential equations in the complex domain.
The meeting “État de la recherche” held in the ENS Lyon in january 1997 aimed at a presentation of the present state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles, corresponding to the lectures presented at the meeting. The paper by D. Cerveau describes the structure of polynomial differential equations in the complex plane focusing on the local analysis around singular points. The second paper, by É. Ghys, is a survey of the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomials or rational maps in complex dimension at least 2. Finally, the lecture of J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree 2 in one complex variable and in particular deals with hyperbolic properties of these polynomials centeredaround the Jakobson theorem. A general introduction gives the rudiments of the history of holomorphic dynamical systems, the aim being to show the reader that these questions are intimately linked and that their interactions are noumerous and fruitful.
[The articles will be announced individually.].

MSC:
00B25 Proceedings of conferences of miscellaneous specific interest
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
37Fxx Dynamical systems over complex numbers
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