%0 Journal Article 
%A Pan Collantes, Antonio Jesús
%A Ruiz Serván, Adrián
%A Muriel Patino, María Concepción
%A Romero, J. L.
%T C∞-symmetries of distributions and integrability
%D 2022
%@ 0022-0396
%U http://hdl.handle.net/10498/31835
%X An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. It is based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the extension of Lie point symmetries to C∞-symmetries for ODEs developed in the recent years. The new structures, named C∞-structures, play a fundamental role in the integrability of the distribution: the knowledge of a C∞-structure for a corank k involutive distribution allows to find its integral manifolds by solving k successive completely integrable Pfaffian equations. These results have important consequences for the integrability of differential equations. In particular, we derive a new procedure to integrate an mth-order ordinary differential equation by splitting the problem into m completely integrable Pfaffian equations. This step-by-step integration procedure is applied to fully integrate several equations that cannot be solved by standard procedures.
%K C∞-structure
%K C∞-symmetry of a distribution
%K Differential equations
%K Frobenius integrability
%K Solvable structure
%K Symmetry of a distribution
%~ Universidad de Cádiz