Displaying similar documents to “Some analogies between number theory and dynamical systems on foliated spaces.”

Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations

José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does...

Multivalued Lyapunov functions for homeomorphisms of the 2-torus

Patrice Le Calvez (2006)

Fundamenta Mathematicae

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Let F be a homeomorphism of 𝕋² = ℝ²/ℤ² isotopic to the identity and f a lift to the universal covering space ℝ². We suppose that κ ∈ H¹(𝕋²,ℝ) is a cohomology class which is positive on the rotation set of f. We prove the existence of a smooth Lyapunov function of f whose derivative lifts a non-vanishing smooth closed form on 𝕋² whose cohomology class is κ.

Universality results on Hurwitz zeta-functions

Antanas Laurinčikas, Renata Macaitienė (2016)

Banach Center Publications

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In the paper, we give a survey of the results on the approximation of analytic functions by shifts of Hurwitz zeta-functions. Theorems of such a kind are called universality theorems. Continuous, discrete and joint universality theorems of Hurwitz zeta-functions are discussed.

A functional relation for Tornheim's double zeta functions

Kazuhiro Onodera (2014)

Acta Arithmetica

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We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta...

Localization of basic characteristic classes

Dirk Töben (2014)

Annales de l’institut Fourier

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We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold M is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type...

The BIC of a singular foliation defined by an abelian group of isometries

Martintxo Saralegi-Aranguren, Robert Wolak (2006)

Annales Polonici Mathematici

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We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology ℍ * p ̅ ( M / ℱ ) is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group...

Bilipschitz invariance of the first transverse characteristic map

Michel Hilsum (2012)

Banach Center Publications

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Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.