Nearly finite Chacon Transformation
\'Elise Janvresse (1), Emmanuel Roy (2), Thierry De La Rue (3) ((1), LAMFA, (2) LAGA, (3) LMRS)
TL;DR
This paper introduces an infinite-measure version of the Chacon transformation and demonstrates that it exhibits a property akin to Minimal Self-Joinings, with minimal invariant Radon measures in its Cartesian powers.
Contribution
It constructs a new infinite-measure Chacon transformation and proves it has minimal self-joining-like properties, extending finite measure results to an infinite measure setting.
Findings
Infinite-measure Chacon transformation constructed
Proven to have minimal invariant Radon measures in Cartesian powers
Extends finite measure properties to infinite measure context
Abstract
We construct an infinite-measure preserving version of Chacon transformation, and prove that it has a property similar to Minimal Self-Joinings in finite measure: its Cartesian powers have as few invariant Radon measures as possible.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematics and Applications · History and Theory of Mathematics