Revisiting Lie integrability by quadratures from a geometric perspective
Volume 110 / 2016
Banach Center Publications 110 (2016), 25-40
MSC: 37J35, 70H06.
DOI: 10.4064/bc110-0-2
Abstract
After a short review of the classical Lie theorem, a finite-dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way are discussed, determining also the number of quadratures needed to integrate the system. The theory is illustrated with examples, and an extension of the theorem where the Lie algebras are replaced by some distributions is also presented.
