Annali di Matematica Pura ed Applicata

, Volume 163, Issue 1, pp 143–160 | Cite as

On the existence of global first integrals in the plane

  • Luisa Mazzi
  • Marco Sabatini


A plane, autonomous, noncritical differential system x′=f(x) of classCk is given. Under a suitable «discreteness» hypothesis on the behavior of orbits, the exeistence of a global first integral as regular as the field (provided k ≠ ω)is proved.


Differential System 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1993

Authors and Affiliations

  • Luisa Mazzi
    • 1
  • Marco Sabatini
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorino
  2. 2.Dipartimento di MatematicaUniversità di TrentoPovo

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