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The meeting, 'Etat de la recherche', held at Ecole Normale Superieure de Lyon, presented the state of the art in the area of holomorphic dynamical systems, emphasizing the unity linking the various sub-domains. This book contains four survey articles corresponding to the talks presented at this meeting.

Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. This text illustrates developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) is included.