Displaying similar documents to “On the Gevrey hypo-ellipticity of sums of squares of vector fields”

Levi-flat invariant sets of holomorphic symplectic mappings

Xianghong Gong (2001)

Annales de l’institut Fourier

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We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant...

A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators

Paulo D. Cordaro, Nicholas Hanges (2009)

Annales de l’institut Fourier

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Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let q be a characteristic point for P . We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that P is analytic hypoelliptic at q . Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained...

Invariant properties of the generalized canonical mappings

Stanisław Janeczko (1999)

Banach Center Publications

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One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.

Relations among analytic functions. II

Edward Bierstone, P. D. Milman (1987)

Annales de l'institut Fourier

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This is a sequel to “Relations among analytic functions I”, , , fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding 𝒞 ∞ solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.