منابع مشابه
Descriptive Kakutani equivalence
We consider a descriptive version of Kakutani equivalence for Borel automorphisms of Polish spaces. Answering a question of Nadkarni, we show that up to this notion, there are exactly two Borel automorphisms: those which are smooth, and those which are not. Using this, we classify all Borel R-flows up to C∞ time-change isomorphism. We then extend the notion of Kakutani equivalence to all (not n...
متن کاملKakutani Equivalence via ~ Α and ~ Β Equivalence In
We show that an even Kakutani equivalence class of Z2 actions is “spanned” by ~ α and ~ β equivalence classes where ~ α = {1+α1, 1+ α2}, ~ β = {1 + β1, 1 + β2} and {1, α −1 i , β −1 i } are rationally independent for i = 1, 2. Namely, given such vectors ~ α and ~ β and two evenly Kakutani equivalent Z2 actions S and T , we show that U is ~ α -equivalent to S and ~ β -equivalent to T . Date: Apr...
متن کاملEven Kakutani Equivalence via Α and Β Equivalence In
In this paper we discuss the relationship between two of the fundamental examples of restricted orbit equivalence: even Kakutani equivalence and α equivalence. Both equivalence relations arise in the context of representations of ergodic and measure preserving Rd actions. The first is related to the Ambrose-Kakutani Theorem [1]: every free, measure preserving and ergodic R action can be represe...
متن کاملEven Kakutani Equivalence and the Loose Block Independence Property for Positive Entropy Z Actions
In this paper we define the loose block independence property for positive entropy Zd actions and extend some of the classical results to higher dimensions. In particular, we prove that two loose block independent actions are even Kakutani equivalent if and only if they have the same entropy. We also prove that for d > 1 the ergodic, isometric extensions of the positive entropy loose block inde...
متن کاملFrom Imitation Games to Kakutani
We give a full proof of the [Kakutani(1941)] fixed point theorem that is brief, elementary, and based on game theoretic concepts. This proof points to a new family of algorithms for computing approximate fixed points. An imitation game is a finite two person normal form game in which the strategy spaces for the two agents are the same and the goal of the second player is to choose the same stra...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2010
ISSN: 1435-9855
DOI: 10.4171/jems/194