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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.

Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. His seminar at the Ecole Polytechnique had major worldwide influence and was the main vector in the development of the theory of dynamical systems in France. His interests covered most aspects of the subject though closest to his heart were the so-called small divisors problems, in particular those related to the stability of quasiperiodic motions. This volume aims to reflect the depth and variety of these interests and the frontier of present research; a frontier shaped decisively by...

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.