A Sampling Theorem for Rotation Numbers of Linear Processes in ²

الأصل · EN

We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in S¹. In particular, the concept of rotation number of a matrix g∈ Gl⁺(2,) can be generalized to a product of a sequence of stationary random matrices in Gl⁺(2,). In this particular case this result provides a counter-part of the Osseledec's multiplicative ergodic theorem which guarantees the existence of Lyapunov exponents. A random sampling theorem is then proved to show that the concept we propose is consistent by discretization in time with the rotation number of continuous linear processes on ².