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  3. Restricted Orbit Equivalence for Actions of Discrete Amenable Groups
  • Cited by 13
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      April 2002
      ISBN:
      9780511549908
      9780521807951
      9780521183857
      DOI:
      https://doi.org/10.1017/CBO9780511549908
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.48kg, 208 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.31kg, 208 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
      Series:
      Cambridge Tracts in Mathematics (146)
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
    Series:
    Cambridge Tracts in Mathematics (146)
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    Book description

    This 2002 monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all these examples simultaneously and gives insight into how to seek further applications. The work is placed in the context of discrete amenable group actions where time is not required to be one-dimensional, making the results applicable to a much wider range of problems and examples.

    Reviews

    Review of the hardback:‘… this profound book … gives an attractive overview and backward look at the restricted orbit equivalence theory for single transformations and other ‘small’ groups.’

    Source: Zentralblatt für Mathematik

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