A part of the conference "Attractors, Foliations, and Limit Cycles".
The talk will consists of two part: real and complex ones.
Normal forms of local families.
Zeros of Abelian integrals.
Polynomial foliations in the complex plane.
Nonlinear Stokes phenomena.
Limit cycles: finiteness theorems and Hilbert-Arnold problem.
Persistence of geometric objects related to polynomial dynamics.
Not only the results, but also the relations between them will be discussed.