Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part

Patrick Bonckaert; Freek Verstringe

Displaying similar documents to “Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part”

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten (2010)

Annales de l’institut Fourier

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We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which...

Surprising properties of centralisers in classical Lie algebras

Oksana Yakimova (2009)

Annales de l’institut Fourier

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Let $𝔤$ be a classical Lie algebra, , either ${𝔤𝔩}_{n}$ , ${𝔰𝔭}_{n}$ , or ${𝔰𝔬}_{n}$ and let $e$ be a nilpotent element of $𝔤$ . We study various properties of the centralisers $𝔤_{e}$ . The first four sections deal with rather elementary questions, like the centre of $𝔤_{e}$ , commuting varieties associated with $𝔤_{e}$ , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on $𝔤_{e}^{*}$ and symmetric invariants of $𝔤_{e}$ .

Minimal nilpotent bases for Goursat distributions of coranks not exceeding six.

Mormul, Piotr (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro (2011)

Annales de l’institut Fourier

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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( $ϕ, Γ$ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( $ϕ, Γ$ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...

Nilpotent control systems.

Elisabeth Remm, Michel Goze (2002)

Revista Matemática Complutense

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We study the class of matrix controlled systems associated to graded filiform nilpotent Lie algebras. This generalizes the non- linear system corresponding to the control of the trails pulled by car.