Two-step coding theorem in the nearly continuous category
Date
2013
Authors
Salvi, Niketa, author
Shipman, Patrick, advisor
Şahin, Ayşe, advisor
Dangelmayr, Gerhard, committee member
Oprea, Iuliana, committee member
Wang, Haonan, committee member
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Abstract
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.
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Subject
flow built under a function
two step flow
nearly continuous