 98356 Giuseppe Gaeta
 Reduction and Equivariant Branching Lemma
without finitedimensional reduction
(69K, Plain TeX)
May 22, 98

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Abstract. In the bifurcation study of nonlinear
evolution PDEs with symmetry, one usually performs first a
reduction to a finite dimensional critical space, thus
obtaining the bifurcation equation (which inherits
symmetries properties from the original problem), and then
employs the symmetry  tipically through the reduction
lemma and/or the equivariant branching lemma  to study
this reduced problem. We argue that one could as well
proceed in the opposite way, i.e. apply bifurcation
analysis on a symmetryreduced problem; this is done using
some general results of Palais for variational analysis of
$G$invariant functionals. Such an approach presents some
delicate points, which we discuss in detail.
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98356.tex