Total convergence or general divergence in Small Divisors

Details Total convergence or general divergence in Small Divisors Total convergence or general divergence in Small Divisors

2000-09-04

arxiv.org/abs/math/0009029v1

Mathematics

Dynamical Systems

Scientific paper

10.1007/s002200100457

We study generic holomorphic families of dynamical systems presenting
problems of small divisors with fixed arithmetic. We prove that we have
convergence for all parameter values or divergence everywhere except for an
exceptional set in the potential theory sense. We illustrate this general
principle in different problems of small divisors.

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