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Borel matrix

Michel Weber (1995)

Commentationes Mathematicae Universitatis Carolinae

We study the Borel summation method. We obtain a general sufficient condition for a given matrix A to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the L p -setting, we establish necessary conditions of the same kind by using Bourgain’s...

Borel summation and splitting of separatrices for the Hénon map

Vassili Gelfreich, David Sauzin (2001)

Annales de l’institut Fourier

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...

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