## Abstract

Let T_{ρ} be a one-sided Bernoulli shift, which acts on the product space (X_{ρ},μ_{ρ}) = Π ^{∞}_{n=1}=(I,ρ) is a finite or countable state space with a probability distribution ρ = {ρ(i)}iεI, ρ(i) > 0, Σ_{iε ρ}(i) = 1. Let also Y_{d} = {1,2, • • • d}, d e N. Suppose p is not homogeneous, i.e. ρ(i) σ(i') for some pair t, i' ε I, and let d > 1. For given such d and p, we construct a uncountable family T_{λ}, λ ε A = A(ρ, d), such that (i) T_{λ} is isomorphic to a d-extension of T_{ρ}, i.e. to a skew product on X_{ρ} × Y _{d} over T_{ρ}. (ii) T_{λ} is an one-sided Markov shift, corresponding to an aperiodic irreducible positively recurrent Markov chain on the infinite countable state space I × N × Y _{d}. (iii) All the shifts T_{λ} λ ε A, are pairwise non-isomorphic. (iv) Each of the shifts T_{λ} λ ε A, is not Isomorphic to one-sided Markov shifts on finite state spaces (even in the case, when I is finite).

Original language | English |
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Pages (from-to) | 273-297 |

Number of pages | 25 |

Journal | Indian Journal of Mathematics |

Volume | 54 |

Issue number | 3 |

State | Published - 1 Dec 2012 |

## Keywords

- One sided markov shifts
- Skew products over bernoulli shifts isomorphism problem

## ASJC Scopus subject areas

- Mathematics (all)