Invariant ideals of local analytic and formal vector fields
Dynamical Systems
2018-11-07 v1
Abstract
The objective of this paper is to analyse analytic invariant sets of analytic ordinary differential equations (ODEs). For this purpose we introduce semi-invariants and invariant ideals as well as the notion of vector fields in Poincare- Dulac normal form (PDNF). We prove that all invariant ideals of a vector field in PDNF are already invariant for its semi-simple linear part. Additionally, this paper provides a natural characterization of invariant ideals via semi-invariants.
Keywords
Cite
@article{arxiv.1811.02389,
title = {Invariant ideals of local analytic and formal vector fields},
author = {Niclas Kruff},
journal= {arXiv preprint arXiv:1811.02389},
year = {2018}
}