About: Bernoulli scheme

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In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal.

Attributes	Values
rdf:type	Thing
rdfs:label	Bernoulli scheme (en)
rdfs:comment	In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal. (en)
sameAs	Bernoulli scheme Bernoulli scheme
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Clarify dbt:Reflist dbt:Short_description dbt:Use_American_English
Subject	Ergodic theory Symbolic dynamics Markov models
gold:hypernym	Generalization
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Bernoulli_scheme?oldid=1069918434&ns=0
Wikipage page ID	2580555 (xsd:integer)
page length (characters) of wiki page	11087 (xsd:nonNegativeInteger)
Wikipage revision ID	1069918434 (xsd:integer)
Link from a Wikipage to another Wikipage	Adjacency matrix Amenable group Anosov diffeomorphism Asymptotic equipartition property Attractor Axiom A Bernoulli process Bernoulli scheme Stationary process Yakov Sinai Σ-algebra Cantor set Cartesian product Ergodic theory Symbolic dynamics Markov models Smoothness Direct product Discrete group Discrete time and continuous time Kullback–Leibler divergence Cylinder set Sample space Shift operator Time-inhomogeneous hidden Bernoulli model Triangle inequality Clique (graph theory) Countable set Dynamical billiards Dynamical system Ornstein isomorphism theorem Partition of a set Independence (probability theory) Symbolic dynamics Exponential object Group action Haar measure Hamming distance Standard probability space Stochastic process Subshift of finite type Kolmogorov automorphism Kakutani's theorem (measure theory) Markov chain Markov partition Mathematics Measure-preserving dynamical system Measure (mathematics) Measure space Random variable
has abstract	In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Bernoulli_scheme
is rdfs:seeAlso of	Ergodicity
is Wikipage redirect of	Bernoulli automorphism Bernoulli probabilistic scheme Bernoulli shift Ornstein's theorem
is Link from a Wikipage to another Wikipage of	Flow (mathematics) List of statistics articles List of stochastic processes topics List of things named after Jakob Bernoulli List of things named after members of the Bernoulli family Bernoulli process Bernoulli scheme Bernoulli trial Catalog of articles in probability theory Jacob Bernoulli Donald Samuel Ornstein Lehmer's conjecture List of probability topics Dyadic transformation Dynamical billiards Ergodic theory Ergodicity Bernoulli automorphism Bernoulli probabilistic scheme Bernoulli shift Kolmogorov's zero–one law Kolmogorov automorphism Markov chain Measure-preserving dynamical system Multiplication theorem

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