The last thirty years were a period of continuous and intense
growth in the subject of dynamical systems. New concepts and
techniques and at the same time new areas of applications of the
theory were found. The 31st session of the Seminaire de
Mathematiques Superieures (SMS) held at the Universite de Montreal
in July 1992 was on dynamical systems having as its center theme
"Bifurcations and periodic orbits of vector fields." This session
of the SMS was a NATO Advanced Study Institute (ASI). This ASI had
the purpose of acquainting the participants with some of the most
recent developments and of stimulating new research around the
chosen center theme. These developments include the major tools of
the new resummation techniques with applications, in particular to
the proof of the non-accumulation of limit-cycles for real-analytic
plane vector fields. One of the aims of the ASI was to bring
together methods from real and complex dy namical systems. There is
a growing awareness that an interplay between real and complex
methods is both useful and necessary for the solution of some of
the problems. Complex techniques become powerful tools which yield
valuable information when applied to the study of the dynamics of
real vector fields. The recent developments show that no rigid
frontiers between disciplines exist and that interesting new
developments occur when ideas and techniques from diverse
disciplines are married. One of the aims of the ASI was to show
these multiple interactions at work."
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