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Maximal entropy measures in dimension zero

100%

Huczek D.

Colloquium Mathematicum

2012

tom 127

nr 1

55-66

We prove that an invertible zero-dimensional dynamical system has an invariant measure of maximal entropy if and only if it is an extension of an asymptotically h-expansive system of equal topological entropy.

Faithful zero-dimensional principal extensions

63%

Downarowicz T., Huczek D.

Studia Mathematica

2012

tom 212

nr 1

1-19

We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Huczek D.

1 Downarowicz T.

2 2012

Wyniki wyszukiwania

Maximal entropy measures in dimension zero

Faithful zero-dimensional principal extensions