Proximality and equidistribution on the Furstenberg boundary

Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and \Gamma a lattice in G. We prove that every \Gamma-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of \Gamma on G/P

A Borel-Cantelli lemma for intermittent interval maps

We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure \mu. Kim showed that there exists a sequence of intervals A_n such that \sum \mu(A_n)=\infty, but \{A_n\} does not satisfy the dynamical Borel-Cantelli lemma, i.e., for almost every x, the set \{n : T^n(x)\in A_n\} is finite. If \sum \Leb(A_n)=\infty, we prove that \{A_n\} satisfies the Borel-Cantelli lemma. Our results apply in particular to some maps T whose correlations are not summable.Comment: 7 page

Khinchin theorem for integral points on quadratic varieties

We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.Comment: 19 page

Probación religiosa de la obediencia

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Prueba religiosa sobre la castidad

ColofónNo v. da port. consta 1956 como ano de reim

Évaluation de l’inflammation conjonctivale chez les porteurs de prothèse oculaire

National audienc