# Bifurcation of critical points for continuous families of C^2 functionals of Fredholm type

Pejsachowicz, Jacobo, Waterstraat, Nils (2013) Bifurcation of critical points for continuous families of C^2 functionals of Fredholm type. Journal of Fixed Point Theory and Applications, 13 (2). pp. 537-560. ISSN 1661-7738. (doi:10.1007/s11784-013-0137-0)

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## Abstract

Given a continuous family of C^2 functionals of Fredholm type, we show that the non-vanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.

Item Type: Article 10.1007/s11784-013-0137-0 Imported from arXiv Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics Nils Waterstraat 03 Nov 2015 16:04 UTC 29 May 2019 16:15 UTC https://kar.kent.ac.uk/id/eprint/51394 (The current URI for this page, for reference purposes)
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