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Prime type III λ Automorphisms: An Instance of Coding Techniques applied to Non-Singular maps

In: Algorithms, Fractals, and Dynamics

Author

Listed:
  • Andrés del Junco

    (University of Tronto, Department of Mathematics)

  • César Silvan

    (Williams College, Department of Mathematics)

Abstract

Rudolph and Silva introduced a notion of minimal self joinings for non-singular auto-morphisms and used it to construct an example T of each Krieger type which commutes only with its powers and has only trivial invariant σ-algebras. Here we show that such examples can be obtained more directly using coding ideas. In fact, coding techniques yield results which do not seem obtainable via joinings, e.g. a complete classification of the factor algebras of T x T. Such coding techniques are quite standard in the context of finite measure-preserving maps but have not, as far as we know, been applied to non-singular maps. In the classical setting the d̄-metric on sequences plays a central role and here we use a weighted version of it. The example T which we work with is a type III λ version of Chacón’s map

Suggested Citation

  • Andrés del Junco & César Silvan, 1995. "Prime type III λ Automorphisms: An Instance of Coding Techniques applied to Non-Singular maps," Springer Books, in: Y. Takahashi (ed.), Algorithms, Fractals, and Dynamics, pages 101-115, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0321-3_9
    DOI: 10.1007/978-1-4613-0321-3_9
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