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The thread of self-organization which is now recognized as
permeating many dynamical transformations in diverse systems around
us seems set to unleash a revolution as influential as that of
Darwin in the last century. Darwin removed the 'originator' of a
species; self-organization now seeks to remove the 'organizer' from
an organism. Methods of nonlinear dynamics have played a crucial
role in opening up this field and if these methods have a
progenitor it is Henri Poi~care (1854 - 1912) whose first
substantial compilation amongst his prolific productio~ was Les
Methodes Nouvelles de la Mecanique Celeste, Vol 1. Thi~
work'aplleared in Paris in 1892, a century ago, thus offering us
the opportunity to celebrate a centenary of this extraordinary
revolutionary of science: M~:of. ~he ex;tensive contributions of
Poincare helped to lay the foundation of this field of nonlinear
dynamics, for _e. xam*lI~e mai:hematic~l theory of . dillJ.
ensions~ . ( qualita. tively) global aspects of ph~ ~~c~ d~~~ics,
topological analysis, . fiXed. pbiilt theo- rems, bifurcation
COIiC~l?ts :{~o ?e u~d later for example for Andronov-Poincare
bifurcation), diffe~!:. Iice' equation mappings in phase spa
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