On the resurgent approach to Ecalle-Voronin's invariants

@article{Dudko2013OnTR,
  title={On the resurgent approach to Ecalle-Voronin's invariants},
  author={Artem Dudko and David Sauzin},
  journal={arXiv: Dynamical Systems},
  year={2013}
}

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References

SHOWING 1-10 OF 16 REFERENCES

Nonlinear analysis with resurgent functions

We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed

On the Stability under Convolution of Resurgent Functions

This article contains a self-contained proof of the stability under convolution of the class of resurgent functions associated with a closed discrete subset of C, under the assumption that , the set

Fixed Point of the Parabolic Renormalization Operator

A global theory of the dynamics of a parabolic germ and some results are presented that show the importance of knowing the local dynamics of the germ and the global theory itself.

Pseudo-groupe d'une singularité de feuilletage holomorphe en dimension deux

Un feuilletage holomorphe singulier, en dimension deux, est localement defini par un champ de vecteur holomorphe a zero isole : les feuilles sont les trajec- toires complexes du champ de vecteur.

Introduction to 1-summability and resurgence

This text is about the mathematical use of certain divergent power series. The rst part is an introduction to 1-summability. The denitions rely on the formal Borel transform and the Laplace transform

On the resurgent approach tó Ecalle-Voronin's invariants, II

  • On the resurgent approach tó Ecalle-Voronin's invariants, II