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Minimal models for $ℤ^{d}$-actions

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Frej B., Kwaśnicka A.

Colloquium Mathematicum

2008

tom 110

nr 2

461-476

We prove that on a metrizable, compact, zero-dimensional space every $ℤ^{d}$-action with no periodic points is measurably isomorphic to a minimal $ℤ^{d}$-action with the same, i.e. affinely homeomorphic, simplex of measures.

A map maintaining the orbits of a given $ℤ^{d}$-action

100%

Frej B., Kwaśnicka A.

Colloquium Mathematicum

2016

tom 143

nr 1

1-15

Giordano et al. (2010) showed that every minimal free $ℤ^{d}$-action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest's (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖{one point} such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free $ℤ^{d}$-action.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Frej B.

2 Kwaśnicka A.

1 2016

1 2008

Wyniki wyszukiwania

Minimal models for $ℤ^{d}$-actions

A map maintaining the orbits of a given $ℤ^{d}$-action