The G-invariant implicit function theorem in infinite dimensions
- 1 January 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 92 (1-2) , 13-30
- https://doi.org/10.1017/s0308210500019909
Abstract
Our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries. The result is sufficiently general to cover a great many applications. It generalizes some earlier work of the author and corrects and improves some work of Vanderbauwhede. We also consider the breaking of symmetries problem and the variational case. Finally, we apply our results to study the periodic solutions of an ordinary differential equation.Keywords
This publication has 12 references indexed in Scilit:
- On the structure of solutions of an equation in catalysis theory when a parameter is largeJournal of Differential Equations, 1980
- Symmetry and bifurcation near families of solutionsJournal of Differential Equations, 1980
- An implicit function theorem with symmetries and its application to nonlinear eigenvalue equationsBulletin of the Australian Mathematical Society, 1980
- Bifurcation and symmetry breaking in applied mathematicsBulletin of the American Mathematical Society, 1980
- Vector MeasuresPublished by American Mathematical Society (AMS) ,1977
- Symplectic v-manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifoldsCommunications on Pure and Applied Mathematics, 1977
- Die L sung der Verzweigungsgleichungen f r nichtlineare EigenwertproblemeMathematische Zeitschrift, 1972
- Measurable, continuous and smooth vectors for semi-groups and group representationsMemoirs of the American Mathematical Society, 1968
- Equivariant Embeddings in Euclidean SpaceAnnals of Mathematics, 1957
- The Topology of Fibre Bundles. (PMS-14)Published by Walter de Gruyter GmbH ,1951