# Borel summation and splitting of separatrices for the Hénon map

Vassili Gelfreich^{[1]}; David Sauzin^{[2]}

- [1] The Steklov Mathematical Institute at St. Petersburg, St. Petersburg (Russie)
- [2] Institut de Mécanique Céleste, Astronomie et systèmes Dynamiques, 77 avenue Denfert-Rochereau, 75014 Paris (France)

Annales de l’institut Fourier (2001)

- Volume: 51, Issue: 2, page 513-567
- ISSN: 0373-0956

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topGelfreich, Vassili, and Sauzin, David. "Borel summation and splitting of separatrices for the Hénon map." Annales de l’institut Fourier 51.2 (2001): 513-567. <http://eudml.org/doc/115924>.

@article{Gelfreich2001,

abstract = {We study two complex invariant manifolds associated with the parabolic fixed point of
the area-preserving Hénon map. A single formal power series corresponds to both of them.
The Borel transform of the formal series defines an analytic germ. We explore the Riemann
surface and singularities of its analytic continuation. In particular we give a complete
description of the “first” singularity and prove that a constant, which describes the
splitting of the invariant manifolds, does not vanish. An interpretation in terms of
Resurgence theory is also given.},

affiliation = {The Steklov Mathematical Institute at St. Petersburg, St. Petersburg (Russie); Institut de Mécanique Céleste, Astronomie et systèmes Dynamiques, 77 avenue Denfert-Rochereau, 75014 Paris (France)},

author = {Gelfreich, Vassili, Sauzin, David},

journal = {Annales de l’institut Fourier},

keywords = {Hénon map; difference equations; splitting of separatrices; Borel summation; Laplace transform; resurgence; quadratic area-preserving map; divergent asymptotic series},

language = {eng},

number = {2},

pages = {513-567},

publisher = {Association des Annales de l'Institut Fourier},

title = {Borel summation and splitting of separatrices for the Hénon map},

url = {http://eudml.org/doc/115924},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Gelfreich, Vassili

AU - Sauzin, David

TI - Borel summation and splitting of separatrices for the Hénon map

JO - Annales de l’institut Fourier

PY - 2001

PB - Association des Annales de l'Institut Fourier

VL - 51

IS - 2

SP - 513

EP - 567

AB - We study two complex invariant manifolds associated with the parabolic fixed point of
the area-preserving Hénon map. A single formal power series corresponds to both of them.
The Borel transform of the formal series defines an analytic germ. We explore the Riemann
surface and singularities of its analytic continuation. In particular we give a complete
description of the “first” singularity and prove that a constant, which describes the
splitting of the invariant manifolds, does not vanish. An interpretation in terms of
Resurgence theory is also given.

LA - eng

KW - Hénon map; difference equations; splitting of separatrices; Borel summation; Laplace transform; resurgence; quadratic area-preserving map; divergent asymptotic series

UR - http://eudml.org/doc/115924

ER -

## References

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