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Galois theory of q -difference equations

Marius van der Put, Marc Reversat (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Choose q ∈ ℂ with 0 < | q | < 1 . The main theme of this paper is the study of linear q -difference equations over the field K of germs of meromorphic functions at 0 . A systematic treatment of classification and moduli is developed. It turns out that a difference module M over K induces in a functorial way a vector bundle v ( M ) on the Tate curve E q : = ℂ * / q ℤ that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification ( [ A t ] ) of the indecomposable vector bundles on the complex Tate...

Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto (2003)

Annales de l’institut Fourier

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

General construction of non-dense disjoint iteration groups on the circle

Krzysztof Ciepliński (2005)

Czechoslovak Mathematical Journal

Let ℱ = { F v 𝕊 1 → 𝕊 1 , v ∈ V } be a disjoint iteration group on the unit circle 𝕊 1 , that is a family of homeomorphisms such that F v 1 ∘ F v 2 = F v 1 + v 2 for v 1 , v 2 ∈ V and each F v either is the identity mapping or has no fixed point ( ( V , + ) is a 2 -divisible nontrivial Abelian group). Denote by L ℱ the set of all cluster points of { F v ( z ) , v ∈ V } for z ∈ 𝕊 1 . In this paper we give a general construction of disjoint iteration groups for which ∅ ≠ L ℱ ≠ 𝕊 1 .

Currently displaying 801 – 820 of 2641