Revisiting Lie integrability by quadratures from a geometric perspective

Volume 110 / 2016

José F. Cariñena, Manuel F. Rañada, Fernando Falceto, Janusz Grabowski 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.

Authors

  • José F. CariñenaDepartamento de Física Teórica and IUMA
    Facultad de Ciencias
    Universidad de Zaragoza
    50009 Zaragoza, Spain
    e-mail
  • Manuel F. RañadaDepartamento de Física Teórica and IUMA
    Facultad de Ciencias
    Universidad de Zaragoza
    50009 Zaragoza, Spain
    e-mail
  • Fernando FalcetoDepartamento de Física Teórica and BIFI
    Facultad de Ciencias
    Universidad de Zaragoza
    50009 Zaragoza, Spain
    e-mail
  • Janusz GrabowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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