Théorie ergodique : classification de certaines transformations réelles
Three results on mixing shapes.
Toeplitz flows with pure point spectrum
We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.
Toeplitz -extensions
Topological conditional entropy
Topological Dynamics of Transformations Induced on the Space of Probability Measures.
Topological Markov chains with dicyclic dimension group.
Topological Pressure for One-Dimensional Holomorphic Dynamical Systems
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.
Transformations cylindriques et mesures finies invariantes
Type cocycles without unbounded gaps
An example of type III cocycle without unbounded gaps of an ergodic probability measure preserving transformation will be shown.