Normal forms of C ∞ vector fields based on the renormalization group
- 1 June 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (6), 062703
- https://doi.org/10.1063/5.0031043
Abstract
The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a vector field into its normal form are obtained by means of the renormalization group method. The dynamics of a given vector field such as the existence of invariant manifolds is investigated via its normal form. The C∞ normal form theory is applied to prove the existence of infinitely many periodic orbits of two dimensional systems, which is not shown from polynomial normal forms.This publication has 8 references indexed in Scilit:
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