Displaying similar documents to “Finiteness property for generalized abelian integrals”

An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay, Edgar Lee Stout (2000)

Annales de l'institut Fourier

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This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

Exponentially long time stability for non-linearizable analytic germs of ( ℂ n , 0 ) .

Timoteo Carletti (2004)

Annales de l’institut Fourier

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We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey- s , s > 0 category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey- s formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin, for the analytic germ.

Symbolic discrepancy and self-similar dynamics

Boris Adamczewski (2004)

Annales de l'Institut Fourier

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We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems. ...

Solvability near the characteristic set for a class of planar vector fields of infinite type

Alberto P. Bergamasco, Abdelhamid Meziani (2005)

Annales de l’institut Fourier

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We study the solvability of equations associated with a complex vector field L in ℝ 2 with C ∞ or C ω coefficients. We assume that L is elliptic everywhere except on a simple and closed curve Σ . We assume that, on Σ , L is of infinite type and that L ∧ L ¯ vanishes to a constant order. The equations considered are of the form L u = p u + f , with f satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of L ∧ L ¯ is > 1 , the equation L u = f is solvable in the C ∞ category but not in the...