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Random permutations and unique fully supported ergodicity for the Euler adic transformation

Sarah Bailey Frick, Karl Petersen (2008)

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

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.

Rank gradient, cost of groups and the rank versus Heegaard genus problem

Miklós Abért, Nikolay Nikolov (2012)

Journal of the European Mathematical Society

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the ‘rank vs. Heegaard genus’ conjecture on hyperbolic 3-manifolds is incompatible with the ‘fixed price problem’ in topological dynamics.

Reflexively representable but not Hilbert representable compact flows and semitopological semigroups

Michael Megrelishvili (2008)

Colloquium Mathematicae

We show that for many natural topological groups G (including the group ℤ of integers) there exist compact metric G-spaces (cascades for G = ℤ) which are reflexively representable but not Hilbert representable. This answers a question of T. Downarowicz. The proof is based on a classical example of W. Rudin and its generalizations. A~crucial step in the proof is our recent result which states that every weakly almost periodic function on a compact G-flow X comes from a G-representation of X on reflexive...

Représentation par automate de fonctions continues de tore

F. Blanchard, B. Host, A. Maass (1996)

Journal de théorie des nombres de Bordeaux

Soient A p = { 0 , , p - 1 } et Z A p × A p un sous-système. Z est une représentation en base p d’une fonction f du tore si pour tout point x du tore, ses développements en base p sont liés par le couplage Z aux développements en base p de f ( x ) . On prouve que si f est représentable en base p alors f ( x ) = ( u x + m p - 1 ) mod 1 , où u et m A p . Réciproquement, toutes les fonctions de ce type sont représentables en base p par un transducteur. On montre finalement que les fonctions du tore qui peuvent être représentées par automate cellulaire sont exclusivement les multiplications...

Rigidity of projective conjugacy for quasiperiodic flows of Koch type

Lennard F. Bakker (2008)

Colloquium Mathematicae

For quasiperiodic flows of Koch type, we exploit an algebraic rigidity of an equivalence relation on flows, called projective conjugacy, to algebraically characterize the deviations from completeness of an absolute invariant of projective conjugacy, called the multiplier group, which describes the generalized symmetries of the flow. We then describe three ways by which two quasiperiodic flows with the same Koch field are projectively conjugate when their multiplier groups are identical. The first...

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