Skip to main content
    • Aa
    • Aa

group shifts and Bernoulli factors

  • MIKE BOYLE (a1) (a2) and MICHAEL SCHRAUDNER (a2)

In this paper, a group shift is an expansive action of on a compact metrizable zero-dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equal-entropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraically equivalent to these Bernoulli factors. A completely positive entropy group (even vector) shift need not be topologically conjugate to a Bernoulli shift, and the Pinsker factor of a vector shift need not split topologically.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] M. Boyle . Factoring factor maps. J. London Math. Soc. (2) 57(2) (1998), 491502.

[2] M. Boyle , D. Lind and D. Rudolph . The automorphism group of a shift of finite type. Trans. Amer. Math. Soc. 306(1) (1988), 71114.

[4] M. Einsiedler and K. Schmidt . The adjoint action of an expansive algebraic $\Z \sp d$ action. Monatsh. Math. 135(3) (2002), 203220.

[6] F. Fagnani . Shifts on compact and discrete Lie groups: algebraic-topological invariants and classification problems. Adv. Math. 127(2) (1997), 283306.

[10] B. Kitchens . Multidimensional convolutional codes. SIAM J. Discrete Math. 15(3) (2002), 367381.

[13] D. Lind and K. Schmidt . Homoclinic points of algebraic $\Z \sp d$-actions. J. Amer. Math. Soc. 12(4) (1999), 953980.

[14] D. Lind , K. Schmidt and T. Ward . Mahler measure and entropy for commuting automorphisms of compact groups. Invent. Math. 101 (1990), 593629.

[15] D. Ornstein and B. Weiss . Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math. 48 (1987), 1141.

[16] W. Parry . Intrinsic Markov chains. Trans. Amer. Math. Soc. 112 (1964), 5566.

[17] D. J. Rudolph and K. Schmidt . Almost block independence and Bernoullicity of $\Z \sp d$-actions by automorphisms of compact abelian groups. Invent. Math. 120(3) (1995), 455488.

[18] D. Rudolph and B. Weiss . Entropy and mixing for amenable group actions. Ann. Math. (2) 151(3) (2000), 11191150.

[19] K. Schmidt . Dynamical Systems of Algebraic Origin. Birkhäuser, Basel, 1995.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 56 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2017. This data will be updated every 24 hours.