Two-step coding theorem in the nearly continuous category - Salvi, Niketa, author; Shipman, Patrick, advisor; Şahin, Ayşe, advisor; Dangelmayr, Gerhard, committee member; Oprea, Iuliana, committee member; Wang, Haonan, committee member (Colorado State University. Libraries, 2013)
In measurable dynamics, one studies the measurable properties of dynamical systems. A recent surge of interest has been to study dynamical systems which have both a measurable and a topological structure. A nearly continuous Z-system consists of a Polish space X with a non-atomic Borel probability measure μ and an ergodic measure-preserving homeomorphism T on X . Let ƒ : X → R be a positive, nearly continuous function bounded away from 0 and ∞. This gives rise to a flow built over T under the function ƒ in the nearly continuous category. Rudolph proved a representation theorem in the 1970's, showing that any measurable flow, where the function ƒ is only assumed to be measure-preserving on a measurable Z-system, can be represented as a flow built under a function where the ceiling function takes only two values. We show that Rudolph's theorem holds in the nearly continuous category.
Keywords: flow built under a function; two step flow; nearly continuous