Real-Formal Orbital Rigidity for Germs of Real Analytic Vector Fields on the Real Plane
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- 作者：Jessica Angélica Jaurez-Rosas
- 关键词：Nondicritic vector fields ; Real ; formal orbital equivalence ; Real ; analytic orbital equivalence ; Real ; formal orbital rigidity ; Desingularization of singularities ; Holonomy group
- 刊名：Journal of Dynamical and Control Systems
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：23
- 期：1
- 页码：89-109
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control;
- 出版者：Springer US
- ISSN：1573-8698
- 卷排序：23
文摘
For \(n \geqslant 2\), we consider \(\mathcal {V}^{\mathbb {R}}_{n}\) the class of germs of real analytic vector fields on \(\left (\mathbb {R}^{2}, \widehat {0}\right )\) with zero (n−1)-jet and nonzero n-jet. We prove, for generic germs of \(\mathcal {V}^{\mathbb {R}}_{n}\), that the real-formal orbital equivalence implies the real-analytic orbital equivalence, that is, the real-formal orbital rigidity takes place. This is the real analytic version of Voronin’s formal orbital rigidity theorem.