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Displaying similar documents to “Uniform foliation associated with the hamiltonian system ℋ n ”

On vector fields in C without a separatrix.

J. Olivares-Vázquez (1992)

Revista Matemática de la Universidad Complutense de Madrid

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A family of germs at 0 of holomorphic vector fields in C without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

On algebraic sets invariant by one-dimensional foliations on 𝐂 P ( 3 )

Marcio G. Soares (1993)

Annales de l'institut Fourier

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We consider the problem of extending the result of J.-P. Jouanolou on the density of singular holomorphic foliations on C P ( 2 ) without algebraic solutions to the case of foliations by curves on C P ( 3 ) . We give an example of a foliation on C P ( 3 ) with no invariant algebraic set (curve or surface) and prove that a dense set of foliations admits no invariant algebraic set.