Topological Invariants of Bifurcation
I will shortly discuss an approach to bifurcation theory based on elliptic topology. The main goal is a construction of an index of bifurcation points for C 1-families of Fredholm maps derived from the index bundle of the family of linearizations along the trivial branch. As illustration, I will present an application to bifurcation of homoclinic solutions of non-autonomous differential equations from a branch of stationary solutions.
KeywordsBifurcation Fredholm maps Index bundle J-homomorphism
Unable to display preview. Download preview PDF.
- M.F. Atiyah, K-Theory. Benjamin, 1967.Google Scholar
- N. Hitchin,Harmonic spinors, Adv. in Math. 14 (1974), 1–55.Google Scholar
- J. Ize, Bifurcation theory for Fredholm operators. Mem. Am. Math.Soc. 174 (1976).Google Scholar
- T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, 1976.Google Scholar
- J. Pejsachowicz, The index bundle and bifurcation theory of Fredholm maps. In preparation.Google Scholar