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Real-Formal Orbital Rigidity for Germs of Real Analytic Vector Fields on the Real Plane

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For n≥2$n \geqslant 2$, we consider Vnℝ$\mathcal {V}^{\mathbb {R}}_{n}$ the class of germs of real analytic vector fields on ℝ2,0̂$\left (\mathbb {R}^{2}, \widehat {0}\right )$ with zero (n−1)-jet and nonzero… Click to show full abstract

For n≥2$n \geqslant 2$, we consider Vnℝ$\mathcal {V}^{\mathbb {R}}_{n}$ the class of germs of real analytic vector fields on ℝ2,0̂$\left (\mathbb {R}^{2}, \widehat {0}\right )$ with zero (n−1)-jet and nonzero n-jet. We prove, for generic germs of Vnℝ$\mathcal {V}^{\mathbb {R}}_{n}$, 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.

Keywords: germs real; real analytic; orbital rigidity; formal orbital; real formal

Journal Title: Journal of Dynamical and Control Systems
Year Published: 2017

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