By Janet Whalen Kammeyer

ISBN-10: 0521807956

ISBN-13: 9780521807951

This monograph deals a wide investigative device in ergodic conception and measurable dynamics. the inducement for this paintings is that one may possibly degree how related dynamical structures are through asking how a lot the time constitution of orbits of 1 approach has to be distorted for it to turn into the opposite. assorted regulations at the allowed distortion will result in assorted constrained orbit equivalence theories. those comprise Ornstein's Isomorphism concept, Kakutani Equivalence concept and an inventory of others. through placing such regulations in an axiomatic framework, a basic process is built that encompasses all of those examples at the same time and provides perception into easy methods to search additional functions.

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**Janet Whalen Kammeyer's Restricted Orbit Equivalence for Actions of Discrete PDF**

This monograph deals a huge investigative device in ergodic concept and measurable dynamics. the inducement for this paintings is that one may possibly degree how related dynamical structures are by means of asking how a lot the time constitution of orbits of 1 approach needs to be distorted for it to turn into the opposite. various regulations at the allowed distortion will result in varied constrained orbit equivalence theories.

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**Extra info for Restricted Orbit Equivalence for Actions of Discrete Amenable Groups**

**Sample text**

Examples 4 & 5 (a equivalences). ,a,,} of nonzero real numbers. ,vn/

On any fiber set F x x, T is again 1-1. We definitely do not expect T to be 1-1 on F x A. It is clear, though, that T is non-singular and, at most, # F to 1. The Ornstein-lVeiss Machinery 51 In particular, if T is y'-to-l at x e X, then Rokhlin lemmas concern the degree to which maps T, as above, can be made 1-1. In particular, within a set F x A, one can look for large subsets S on which T is 1-1. We will ask that S be large in a rather strong sense. For S £ F x A, we get a counting function, defined on X, given by Of course (cx/i)(S)= / cs{x)dii(x).

Certainly mKi-equivalence refines even Kakutani equivalence. 6 applies here as well to say the group A5 is an mKi invariant. Hence each even Kakutani equivalence class is cut into at least countably many mKi classes. In [8] it is shown that in one dimension, and for the "loosely Bernoulli" class (the mK -finitely determined class), this is the full refinement. That argument will push through to all dimensions. As a consequence of the construction in [15] there are other mK classes which contain uncountably infinitely many mKi classes.

### Restricted Orbit Equivalence for Actions of Discrete Amenable Groups by Janet Whalen Kammeyer

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