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.
               
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