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Endomorphisms of symbolic algebraic varieties

Misha Gromov (1999)

Journal of the European Mathematical Society

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...

Equations of Lax type with a triple bracket.

Raúl Felipe, Raúl Velásquez (1998)

Extracta Mathematicae

Equations with several brackets arose originally in the works of Brockett [2], [3] (for ordinary differential equations) and Felipe [5] (for partial differential equations) of double bracket equations of Lax type. The purpose of this note is to study triple bracket equations of the form:∂L / ∂t = [L,[L,[L,P]]]. deal with some algebraic properties of these equations, in particular we show that, as in the classical case, they are related to the presence of an infinite sequence of first integrals....

Existence et équidistribution des matrices de dénominateur n dans les groupes unitaires et orthogonaux

Antonin Guilloux (2008)

Annales de l’institut Fourier

Soit G un groupe défini sur les rationnels, simplement connexe, -quasisimple et compact sur . On étudie des suites de sous-ensembles des points rationnels de G définis par des conditions sur leur projection dans le groupe des adèles finies de G . Nous montrons dans ce cadre un résultat d’équirépartition vers la probabilité de Haar sur le groupe des points réels. On utilise pour cela des propriétés de mélange de l’action du groupe des points adéliques G ( 𝔸 ) sur l’espace L 2 ( G ( 𝔸 ) / G ( ) ) . Pour illustrer ce résultat,...

Existence of permanent and breaking waves for a shallow water equation : a geometric approach

Adrian Constantin (2000)

Annales de l'institut Fourier

The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...

Exponential functionals of brownian motion and class-one Whittaker functions

Fabrice Baudoin, Neil O’Connell (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider exponential functionals of a brownian motion with drift in ℝn, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on the law of...

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