Hasard et déterminisme : une approche mathématique
Strongly Mixing g-Measures
Interval Exchange Transformations.
Strongly Mixing g-Measures.
Généralisation d'un lemme de « découpage » de Rokhlin
On the countable generator theorem
Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T.
The M/M/1 queue is Bernoulli
The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result...
Billiards in Polygons
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
Eine Bemerkung zur topologischen Entropie.
Stricte ergodicité des échanges d'intervalles.
Induktive Limiten endlich erzeugter freier Moduln.
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