**山中祥五 氏**

**2019年6月27日(木) 15時00分**

**総合研究10号館317号室(セミナー室)**

We consider systems of differential equations with equilibrium points. These systems are formally transformed to Poincaré-Dulac normal forms, but the normalization may not be analytic. Such an analytic normalization is a classical problem that dates back to Poincaré. Zung [2] proved that analytically integrable systems of differential equations have analytic normalizations. Nonintegrability and nonexistence of analytic normalizations are equivalent when the resonance degree is less than two since their Poincaré-Dulac normal forms are integrable [1]. In this talk, we prove that a special class of two-dimensional systems whose resonance degree is one have no analytic normalizations so that they are not integrable.[1] S. Yamanaka, Local integrability of Poincaré-Dulac normal forms, Regul. Chaotic. Dyn. 23 (2018), 933–947.

[2] N. T. Zung, Convergence versus integrability in Poincaré-Dulac normal forms, Math. Res. Lett. 9 (2002), 217–228.

Last modified: Wed Jan 16 18:03:30 JST 2019