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Nearly finite Chacon transformation. (Transformation de Chacon Presque finie.) (English) Zbl 1435.37013
The authors [Isr. J. Math. 224, 1–37 (2018; Zbl 1406.37011)] and A. I. Danilenko [Isr. J. Math. 228, No. 1, 21–51 (2018; Zbl 1403.28015)] studied some important structural concepts of minimal self-joinings and their extensions to the setting of infinite measure-preserving transformations.
Here such a system is constructed. Its Cartesian powers have as few invariant measures as it is possible to have in this setting. To avoid some of the pathologies of infinite measure, like the infinite sum of Dirac point masses along the orbit of a point, the attention is focused on a topological setting and on Radon measures. The construction is a rank-one transformation dubbed nearly finite Chacon transformation, via a procedure that mimics aspects of the probability-preserving Chacon transformation [R. V. Chacon, Proc. Am. Math. Soc. 22, 559–562 (1969; Zbl 0186.37203)].

37A40 Nonsingular (and infinite-measure preserving) transformations
37A05 Dynamical aspects of measure-preserving transformations
Full Text: DOI
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