Finite ergodic index and asymmetry for infinite measure preserving\n actions

2014/12/13 by Alexandre I. Danilenko, Danilenko, Alexandre I.
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1412.4257

openalex publication_date 2014/12/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Given k>0 and an Abelian countable discrete group G with elements of\ninfinite order, we construct (i) rigid funny rank-one infinite measure\npreserving (i.m.p.) G-actions of ergodic index k, (ii) 0-type funny\nrank-one i.m.p. G-actions of ergodic index k, (iii) funny rank-one i.m.p.\nG-actions T of ergodic index 2 such that the product T\× T^-1 is\nnot ergodic. It is shown that T\× T^-1 is conservative for each funny\nrank-one G-action T.\n

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