Global C∞ Integrability of Cubic–Linear Polynomial Differential Systems
-
-
[1] Chizhou University
Chizhou University
China
-
[2] Shanghai Jiao Tong University
Shanghai Jiao Tong University
China
-
- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 1, 2014, págs. 73-87
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
-
Resumen
The cubic–linear polynomial differential systems having at least one finite singularity are affine equivalent to the systems of the form x = P(x, y) = bx + cy + dx2 + exy + f y2 + gx3 + hx2 y + ixy2 + jy3, y = Q(x, y), with g2 + h2 + i 2 + j 2 = 0 (otherwise it is quadratic–linear), and Q(x, y) is either x or y. In this paper we classify all the cubic–linear systems with Q(x, y) = y which have a global C∞ first integral. Meanwhile we obtain some partial results on the existence of global analytic first integrals. For proving our results we will use the local characterization of first integrals, partition of unity in R2, smoothness of first integrals in canonical regions and so on.
