We discuss local and formal Darboux first integrals of analytic differential systems, using the theory of Poincaré-Dulac normal forms, and we study the effect of local Darboux integrability on analytic normalization. Moreover we determine local restrictions on classical Darboux integrability of polynomial systems. © 2013 Elsevier Masson SAS.
- Analytic differential system
- Local Darboux first integral
- Poincaré-Dulac normal form
- Polynomial differential system