## On the singularities of divergent majorant series arising form normal from theory.(English)Zbl 0723.34037

Summary: The use of majorant series in the theory of normal forms of Hamiltonian systems, symplectic maps of $${\mathbb{R}}^{2d}$$ or complex analytic dynamical systems leads to stability estimates for exponentially long time scales. We discuss the singularities structure of the generating function of a majorant series which is naturally derived from the study of asymptotic series of normal forms theory. Moreover, we prove an asymptotic estimate for the normal forms arising in the study of parabolic Julia sets.

### MSC:

 34E05 Asymptotic expansions of solutions to ordinary differential equations 37C75 Stability theory for smooth dynamical systems 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 70H99 Hamiltonian and Lagrangian mechanics