On Infinite Transformations with Maximal Control of Ergodic Two-fold\n Product Powers

2014/02/07 by Terrence Adams, Adams, Terrence M., Cesar E. Silva +1
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1402.1818

openalex publication_date 2014/02/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study the rich behavior of ergodicity and conservativity of Cartesian\nproducts of infinite measure preserving transformations. A class of\ntransformations is constructed such that for any subset R\⊂ mathbb Q\∩\n(0,1) there exists T in this class such that T^p\× T^q is ergodic if\nand only if \(p)/(q) \∈ R. This contrasts with the finite measure\npreserving case where T^p\× T^q is ergodic for all nonzero p and q if\nand only if T\× T is ergodic. We also show that our class is rich in the\nbehavior of conservative products.\n For each positive integer k, a family of rank-one infinite measure\npreserving transformations is constructed which have ergodic index k, but\ninfinite conservative index.\n

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