Abstract
The renormalization group (RG) method for differential equations is one of the perturbation methods for obtaining solutions which approximate exact solutions for a long time interval. This article shows that, for a differential equation associated with a given vector field on a manifold, a family of approximate solutions obtained by the RG method defines a vector field which is close to the original vector field in the $C^1$ topology under appropriate assumptions. Furthermore, some topological properties of the original vector field, such as the existence of a normally hyperbolic invariant manifold and its stability, are shown to be inherited from those of the RG equation. This fact is applied to the bifurcation theory.
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.
