Invariant measures for ergodic semigroups of operators

Mean Ergodic Theorems for C0 Semigroups of Continuous Linear Operators

In this paper we obtained mean ergodic theorems for semigroups of bounded linear or continuous affine linear operators on a Banach space under non-power bounded conditions. We then apply them to the wave equation and the system of elasticity to show that the mean of their solutions converges to their equilibriums.

Ergodic Theory for C-semigroups

We deene the ergodicity of C-semigroups in this paper, and then characterize the generators.

Absolutely Continuous, Invariant Measures for Dissipative, Ergodic Transformations

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these. Introduction Let (X,B, m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-absolu...

On the space of ergodic invariant measures of unipotent flows

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

Existence of Bounded Invariant Measures in Ergodic Theory