About: Markov odometer

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In mathematics, a Markov odometer is a certain type of topological dynamical system. It plays a fundamental role in ergodic theory and especially in orbit theory of dynamical systems, since a theorem of H. Dye asserts that every ergodic nonsingular transformation is orbit-equivalent to a Markov odometer. The general form, which is called "Markov odometer", can be constructed through Bratteli–Vershik diagram to define Bratteli–Vershik compactum space together with a corresponding transformation.

Attributes	Values
rdfs:label	Markov odometer (en)
rdfs:comment	In mathematics, a Markov odometer is a certain type of topological dynamical system. It plays a fundamental role in ergodic theory and especially in orbit theory of dynamical systems, since a theorem of H. Dye asserts that every ergodic nonsingular transformation is orbit-equivalent to a Markov odometer. The general form, which is called "Markov odometer", can be constructed through Bratteli–Vershik diagram to define Bratteli–Vershik compactum space together with a corresponding transformation. (en)
foaf:depiction
dcterms:subject	Dynamical systems Ergodic theory
Wikipage page ID	56880139 (xsd:integer)
Wikipage revision ID	1108087905 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Product topology Product measure Topological dynamical system Cylinder set Degree (graph theory) Dynamical system Compact space Conservative system Measure (mathematics) Orbit (dynamics) Bernoulli process Measure (mathematics) Stochastic matrix Measure-preserving dynamical system Topological group Haar measure American Mathematical Society Ergodic Ergodic theory Bratteli–Vershik diagram Topological entropy Abelian group Abelian sandpile model Dynamical systems Ergodic theory Homeomorphism Discrete space Graph Laplacian Metric space Metric topology Dyadic integers Atomic measure Product space Henry Abel Dye
sameAs	Markov odometer Markov odometer
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Dyadic_odometer.svg?width=300
has abstract	In mathematics, a Markov odometer is a certain type of topological dynamical system. It plays a fundamental role in ergodic theory and especially in orbit theory of dynamical systems, since a theorem of H. Dye asserts that every ergodic nonsingular transformation is orbit-equivalent to a Markov odometer. The basic example of such system is the "nonsingular odometer", which is an additive topological group defined on the product space of discrete spaces, induced by addition defined as , where . This group can be endowed with the structure of a dynamical system; the result is a conservative dynamical system. The general form, which is called "Markov odometer", can be constructed through Bratteli–Vershik diagram to define Bratteli–Vershik compactum space together with a corresponding transformation. (en)
prov:wasDerivedFrom	wikipedia-en:Markov_odometer?oldid=1108087905&ns=0
page length (characters) of wiki page	13524 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Markov_odometer
is Link from a Wikipage to another Wikipage of	Cylinder set Von Neumann-Kakutani adding machine Interval exchange transformation Nonsingular odometer Odometer (disambiguation) Ergodicity Bernoulli process Hall word Bratteli–Vershik diagram Karen Brucks Adding machine (disambiguation) Markov chain List of things named after Andrey Markov Markov Odometer Dyadic adding machine Dyadic odometer Markov compactum Von Neumann–Kakutani adding machine
is Wikipage redirect of	Von Neumann-Kakutani adding machine Nonsingular odometer Markov Odometer Dyadic adding machine Dyadic odometer Markov compactum Von Neumann–Kakutani adding machine
is Wikipage disambiguates of	Odometer (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Markov_odometer

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