12 citations · 27 across the 10 of their papers we have counts for
4 papers · 1 filter
Autonomous second-order ODEs: a geometric approach
Antonio J. Pan-Collantes, Jose A. Alvarez-Garcia
Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established…
Integration of first-order ODEs by Jacobi fields
A. J. Pan-Collantes, J. A. Alvarez-Garcia
A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmet…
Surfaces associated with first-order ODEs
Antonio J. Pan-Collantes, José A. Álvarez-García
A link between first-order ordinary differential equations (ODEs) and 2-dimensional Riemannian manifolds is explored. Given a first-order ODE, an associated Riemannian metric on th…
-structures in the integration of involutive distributions
A. J. Pan-Collantes, C. Muriel, A. Ruiz +1
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…