Displaying similar documents to “Generalized Staircases: Recurrence and Symmetry”

Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

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We consider representations of the fundamental group of the four punctured sphere into SL ( 2 , ) . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from SU ( 2 ) -representations. We prove the absence of invariant affine structure...

Decompositions of an Abelian surface and quadratic forms

Shouhei Ma (2011)

Annales de l’institut Fourier

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When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

Stable norms of non-orientable surfaces

Florent Balacheff, Daniel Massart (2008)

Annales de l’institut Fourier

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We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Veronica Baker, Marcy Barge, Jaroslaw Kwapisz (2006)

Annales de l’institut Fourier

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This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

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Let K be a global field of characteristic not 2. Let Z = H G be a symmetric variety defined over K and S a finite set of places of K . We obtain counting and equidistribution results for the S-integral points of Z . Our results are effective when K is a number field.