Mixing constructions with infinite invariant measure and spectral\n multiplicities

2009/08/12 by Alexandre I. Danilenko, Danilenko, Alexandre I., Valery V. Ryzhikov +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #37A #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0908.1643

openalex publication_date 2009/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce high staircase infinite measure preserving transformations and\nprove that they are mixing under a restricted growth condition. This is used to\n(i) realize each subset E\⊂ Bbb N\∪ \∞ as the set of essential\nvalues of the multiplicity function for the Koopman operator of a mixing\nergodic infinite measure preserving transformation, (ii) construct mixing power\nweakly mixing infinite measure preserving transformations, (iii) construct\nmixing Poissonian automorphisms with a simple spectrum, etc.\n

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