Displaying similar documents to “Universal isomonodromic deformations of meromorphic rank 2 connections on curves”

Moduli spaces for linear differential equations and the Painlevé equations

Marius van der Put, Masa-Hiko Saito (2009)

Annales de l’institut Fourier

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A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map R H : ℳ → ℛ , where ℳ is a moduli space of connections and ℛ , , is a moduli space for analytic data (, ordinary monodromy, Stokes matrices and links). The assumption that the fibres of R H (, the isomonodromic families) have dimension one, leads to ten moduli spaces ℳ . The induced Painlevé equations are computed explicitly. Except for the...

Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

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We consider representations of the fundamental group of the four punctured sphere into SL ( 2 , ℂ ) . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from SU ( 2 ) -representations. We prove the absence of invariant affine structure...

Finite determinacy of dicritical singularities in ( ℂ 2 , 0 )

Gabriel Calsamiglia-Mendlewicz (2007)

Annales de l’institut Fourier

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For germs of singularities of holomorphic foliations in ( ℂ 2 , 0 ) which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

A note on M. Soares’ bounds

Eduardo Esteves, Israel Vainsencher (2006)

Annales de l’institut Fourier

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We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of ℂℙ n .

Normalization of bundle holomorphic contractions and applications to dynamics

François Berteloot, Christophe Dupont, Laura Molino (2008)

Annales de l’institut Fourier

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We establish a Poincaré-Dulac theorem for sequences ( G n ) n ∈ ℤ of holomorphic contractions whose differentials d 0 G n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps. Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of ℂ ℙ k . In this context, our normalization result allows to estimate precisely...