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Actions of finite rank: weak rational ergodicity and partial rigidity

Published online by Cambridge University Press:  13 April 2015

ALEXANDRE I. DANILENKO
ALEXANDRE I. DANILENKO*
Affiliation:
Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61164, Ukraine email alexandre.danilenko@gmail.com
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Abstract

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A simple proof of the fact that each rank-one infinite measure preserving (i.m.p.) transformation is subsequence weakly rationally ergodic is found. Some classes of funny rank-one i.m.p. actions of Abelian groups are shown to be subsequence weakly rationally ergodic. A constructive definition of finite funny rank for actions of arbitrary infinite countable groups is given. It is shown that the ergodic i.m.p. transformations of balanced finite funny rank are subsequence weakly rationally ergodic. It is shown that the ergodic probability preserving transformations of exact finite rank, the ergodic Bratteli–Vershik maps corresponding to the ‘consecutively ordered’ Bratteli diagrams of finite rank, some their generalizations and the ergodic interval exchange transformations are partially rigid.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 7 , October 2016, pp. 2138 - 2171
Copyright
© Cambridge University Press, 2015 

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