an:06017079
Zbl 1235.35007
Bergamasco, Adalberto P.; Dattori da Silva, Paulo L.
Solvability in the large for a class of complex vector fields on the cylinder
EN
Bull. Sci. Math. 136, No. 2, 162-171 (2012).
00296628
2012
j
35A01 35F05
global solvability; condition \((\mathcal P)\); Sussmann orbits; \(\mathcal L\)-convexity for supports
Summary: This work deals with global solvability of a class of complex vector fields of the form \(\mathcal L = \partial /\partial t + (a(x,t) + ib(x,t))\partial /\partial x\), where \(a\) and \(b\) are real-valued \(C^{\infty }\) functions, defined on the cylinder \(\varOmega = \mathbb R \times S^{1}\). Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of \(\mathcal L\)-convexity for supports is investigated.