Escape of mass and entropy for diagonal flows in real rank one situations

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چکیده

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RANK ONE Zd ACTIONS AND DIRECTIONAL ENTROPY

Rank one transformations play a central role in the theory of ergodic measure preserving transformations. Having first been identified as a distinct class by Chacon in [3], their properties have been studied extensively (see for example [1], [7], [11], [6]). Rank one transformations have also served as an important tool for exploring the range of possible behavior of measure preserving transfor...

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ALGEBRAIC Zd-ACTIONS OF ENTROPY RANK ONE

We investigate algebraic Z-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of ...

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Algebraic Z-actions of Entropy Rank One

We investigate algebraic Zd-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of...

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ژورنال

عنوان ژورنال: Israel Journal of Mathematics

سال: 2015

ISSN: 0021-2172,1565-8511

DOI: 10.1007/s11856-015-1252-y