Corpus ID: 235458402

On integral conditions for the existence of first integrals analytic saddle singularities

  title={On integral conditions for the existence of first integrals analytic saddle singularities},
  author={V. Le'on and B. Sc'ardua},
We study one-parameter analytic integrable deformations of the germ of 2 × (n − 2)-type complex saddle singularity given by d(xy) = 0 at the origin 0 ∈ C × C. Such a deformation writes ω = d(xy) + ∞ ∑ j=1 tωj where t ∈ C, 0 is the parameter of the deformation and the coefficients ωj are holomorphic one-forms in some neighborhood of the origin 0 ∈ C. We prove that, under a nondegeneracy condition of the singular set of the deformation, with respect to the fibration d(xy) = 0, the existence of a… Expand


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