RT journal article
T1 C∞-structures in the integration of involutive distributions
A1 Pan Collantes, Antonio Jesús
A1 Ruiz Serván, Adrián
A1 Muriel Patino, María Concepción
A1 Romero Romero, Juan Luis
A2 Matemáticas
K1 symmetry of a distribution
K1 solvable structure
K1 C∞-symmetry of a distribution
K1 C∞-structure
K1 integrating factor
K1 differential equations
AB For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a systematic procedure of integration via Pfaffian equations that are integrable by quadratures. In this paper structures more general than solvable structures (named C∞-structures) are considered. The symmetry condition in the concept of solvable structure is weakened for C∞-structures by requiring their vector fields be just C∞-symmetries. For C∞structures there is also an integration procedure, but the corresponding Pfaffian equations, although completely integrable, are not necessarily integrable by quadratures. The well-known result on the relationship between integrating factors and Lie point symmetries for first-order ODEs is generalized for C∞-structures and involutive distributions of arbitrary corank by introducing symmetrizing factors. The role of these symmetrizing factors on the integrability by quadratures of the Pfaffian equations associated with the C∞-structure is also established. Some examples that show how these objects and results can be applied in practice are also presented.
SN 1402-4896
YR 2023
FD 2023-05-12
LK http://hdl.handle.net/10498/32130
UL http://hdl.handle.net/10498/32130
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026