Hipoelipticidade, resolubilidade e formas normais para campos vetoriais no toro

Abstract

The main aim of this work is to study a class of real vector elds de ned on a torus, where the concepts of global hypoellipticity, global C1 solvability and reduction to its normal form are equivalents. We also study a family of commuting vector fields that can be converted into a family of constant vector fields provided that there is one of them which its transpose operator is given by a hypoelliptic operator. We also provide some applications on the global hypoellipticity property for a class of sublaplaceans. This work was based on articles [11] and [12] from Gerson Petronilho.