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Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar (2014)

Open Mathematics

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

Fractal representation of the attractive lamination of an automorphism of the free group

Pierre Arnoux, Valérie Berthé, Arnaud Hilion, Anne Siegel (2006)

Annales de l’institut Fourier

In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...

Fractions continues hermitiennes et billard hyperbolique

Pierrick Meignen (1998)

Journal de théorie des nombres de Bordeaux

Nous proposons de formaliser une méthode d’approximation diophantienne dans en considérant l’action de P G L 2 ( ) sur le demi-plan complexe. On retrouvera le thème classique de la connexion entre développement en fractions continues et flots géodésiques modélisé ici par un billard hyperbolique.

Fragmentable mappings and CHART groups

Warren B. Moors (2016)

Fundamenta Mathematicae

The purpose of this note is two-fold: firstly, to give a new and interesting result concerning separate and joint continuity, and secondly, to give a stream-lined (and self-contained) proof of the fact that "tame" CHART groups are topological groups.

Fraïssé structures and a conjecture of Furstenberg

Dana Bartošová, Andy Zucker (2019)

Commentationes Mathematicae Universitatis Carolinae

We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference between S ( G ) , the Samuel compactification, and E ( M ( G ) ) , the enveloping semigroup of the universal minimal flow. We resolve Furstenberg’s problem for several automorphism groups and give a detailed study in the case of G = S , leading us to define and investigate several new types...

Fredholm theory and transversality for the parametrized and for the S 1 -invariant symplectic action

Frédéric Bourgeois, Alexandru Oancea (2010)

Journal of the European Mathematical Society

We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the L 2 -gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S 1 -invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define S 1 -equivariant...

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