Abstract
A $C^0$ theory of finite determination of bifurcation problems is presented in this paper which supplements a corresponding $C^\infty$ theory of Golubitsky and Schaeffer. Finite determination of both bifurcation diagrams and stability properties of branches is considered. $C^0$ finite determination of bifurcation diagrams is shown to follow from an analytic-geometric nondegenracy condition which is modelled on a criterion of Kuo, rather than an algebraic condition of the type found in the $C^\infty$ theory. The class of “quasi-homogeneous” bifurcation problems, which contains bifurcation problems previously studied by McLeod and Sattinger and Landman and Rosenblat using more classical methods, is introduced and shown to admit a simplified and computable nondegeneracy condition which suffices to ensure finite determination of the bifurcation diagram. The results of the $C^0$ theory are compared with those of the $C^\infty$ theory and are found to be a distinct improvement in some cases.Two different notion...
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
