Ergodic theory of multidimensional random dynamical systems .

摘要

Given a random dynamical system T constructed from Jablonski transformations, consider its Perron-Frobenius operator PT. We prove a weak form of the Lasota-York inequality for PT and thereby prove the existence of BV-invariant densities for T. Using the Spectral Decomposition Theorem we prove that the support of an invariant density is open a.e. and give conditions such that the invariant density for T is unique. We study the asymptotic behavior of the Markov operator PT, especially when T has a unique absolutely continuous invariant measure (ACIM). Under the assumption of uniqueness, we obtain spectral stability in the sense of Keller. As an application, we can use Ulam's method to approximate the invariant density of PT.