98-356 Giuseppe Gaeta

Reduction and Equivariant Branching Lemma without finite-dimensional 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 symmetry-reduced 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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