Persistent cycles for holomorphic foliations having a meromorphic first integral. (English) Zbl 0681.58032

Gómez-Mont, Xavier; Muciño, Jesús

Holomorphic dynamics, Proc. 2nd Int. Colloq. Dyn. Syst., Mexico City/Mex. 1986, Lect. Notes Math. 1345, 129-162 (1988).

[For the entire collection see Zbl 0653.00010.]
This paper contains the following sections: 1. The Space of Codimension One Holomorphic Foliations. 1.1 Codimension one holomorphic foliations. 1.2 Projective spaces. 1.3 Families of foliations. 2. First Variations of Holomorphic Foliations. 2.1 First variations and T Fol (M,L). 2.2 First variations of holonomy maps. 2.3 Persistent cycles under deformations. 3. Good Meromorphic First Integrals. 3.1 Lefschetz’s pencils. 3.2 Good meromorphic first integrals. 4. The Iliashenko Curves. 4.1 The Iliashenko curves. 4.2 The conics associated to the indeterminacy locus.

MSC:

37G15	Bifurcations of limit cycles and periodic orbits in dynamical systems
58E30	Variational principles in infinite-dimensional spaces
30D99	Entire and meromorphic functions of one complex variable, and related topics

Keywords:

holomorphic foliations; Projective spaces; First variations; cycles; meromorphic first integrals; Iliashenko Curves; Iliashenko curves

Citations:

Zbl 0653.00010