This paper gives a topological characterization of Diophantine and recurrent laminations on surfaces. It also establishes an upper bound for the number of ergodic components of a measured foliation, in terms of limits of the corresponding geodesic ray in Mg,n. Taken together, these results give a new approach to Masur’s theorem on unique ergodicity. Teichmüller rays. Let Mg,n denote the moduli ...

This letter investigates a single-server discrete-time queuing system with single-slot service times. For a broad class of arrival processes, a closed-form expression for the mean queue content in steady state is obtained. Apart from being stationary ergodic, the arrival process adheres to a regeneration property when there are no arrivals in a slot. Well-studied arrival processes such as autor...

We consider the integrated density of states, k(E)9 of a general operator on /2(Z ) of the form h = hQ + v, where (h0u)(n) = Σ ( + 0 ancl l ϋ = ι (vu)(n) = υ(n)u(n\ where v is a general bounded ergodic stationary process on Z. We show that \k(E) k(E'}\ g C[log(|£ E'\Y when \E ~ £'| ̂ i The key is a "Thouless formula for the strip."

In this note we consider dynamical systems (X, G) on a Cantor set X satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems (X1, G1) and (X2, G2) are orbit equivalent if and only if their full groups are isomorphic as abstract groups. This result is a topological version of the well-known D...

Oseledets’ celebrated Multiplicative Ergodic Theorem (MET) [V.I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210.] is concerned with the exponential growth rates of vectors under the action of a linear cocycle on Rd. When the linear actions are invertible, the MET guarantees an almost-everywhere poi...

Let $ G = \prod_{i 1}^{\mathsf r} G_i be a product of simple real algebraic groups rank one and \Gamma an Anosov subgroup with respect to minimal parabolic subgroup. For each \mathsf v in the interior positive Weyl chamber, let \mathscr R_ v\subset \Gamma\backslash denote Borel subset all points recurrent \exp (\mathbb R_+ v) $-orbits. maximal horospherical N $, we show that $-action on {\maths...