Generically Mañé set supports uniquely ergodic measure for residual cohomology class

Every Ergodic Measure Is Uniquely Maximizing

Let Mφ denote the set of Borel probability measures invariant under a topological action φ on a compact metrizable space X. For a continuous function f : X → R, a measure μ ∈ Mφ is called f -maximizing if ∫ f dμ = sup{ ∫ f dm : m ∈Mφ}. It is shown that if μ is any ergodic measure in Mφ, then there exists a continuous function whose unique maximizing measure is μ. More generally, if E is a non-e...

A Uniquely Ergodic Cellular Automaton

We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on the self-simulating automaton of Gács. We also prove related results of dynamical and computational nature, including the undecidability of unique ergodicity,...

Topological Mixing and Uniquely Ergodic Systems

Every ergodic transformation (X, 7, :~,/z) has an isomorphic system (Y, U, ~, v) which is uniquely ergodic and topologically mixing.

Cohomology on Toric Varieties and Local Cohomology with Monomial Supports

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The ith local cohom...

Existence of Non-uniform Cocycles on Uniquely Ergodic Systems