Coexistence of Uniquely Ergodic Subsystems of Interval Mapping

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Survival and Coexistence for a Multitype

We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside o...

A Characterization of the Uniquely Ergodic Endomorphisms of the Circle

We characterize the uniquely ergodic endomorphisms of the circle in terms of their periodic orbits. Let /: S1 -• S1 be a continuous endomorphism of the circle S1 . Denote by F: R —► R its lifting to the universal covering space. Then, for all x £ R, F satisfies F(x + 1) = F(x) + k for some k £ Z. The number k is called the degree of / (when necessary this number will also be called the degree o...

A Note on Noncommutative Unique Ergodicity and Weighted Means

converge to ET (x) in A for any x ∈ A, as n → ∞, here ET is an projection of A to the fixed point subspace of T . Note that when T is a completely positive mapping then ET is a conditional expectation. We provide an example of uniquely ergodic dynamical system relative its fixed point subspace, for which ET is not a conditional expectation. It is also constructed a uniquely ergodic entangled Ma...

Affine Interval Exchange Transformations with Flips and Wandering Intervals

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.