Abstract
We give a new proof for the existence of a C k -center manifold at a nonhyperbolic equilibrium point of a finite-dimensional vector field of class C k . The problem is reduced to a fixed point problem on a scale of Banach spaces; these Banach spaces consist of mappings with a certain maximal exponential growth at infinity. We give conditions under which there is a unique fixed point depending differentiably on the parameters; the main difficulty is that the mappings under consideration become only differentiable after composition with appropriate embeddings on the scale of Banach spaces.
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.
