Inverses, powers and cartesian products of topologically deterministic maps

Michael Hochman; Artur Siemaszko

Inverses, powers and cartesian products of topologically deterministic maps

Michael Hochman^*
, Artur Siemaszko

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that if (X, T) is a topological dynamical system which is deterministic in the sense of Kamiński, Siemaszko and Szymański then (X, T ^-1) and (X × X, T × T) need not be deterministic in this sense. However if (X × X, T × T) is deterministic then (X, T ⁿ) is deterministic for all n ∈ ℕ \ {0}.

Original language	English
Pages (from-to)	189-198
Number of pages	10
Journal	Topological Methods in Nonlinear Analysis
Volume	39
Issue number	1
State	Published - 2012
Externally published	Yes

Keywords

Recurrence
Topological determinism
Topological dynamics

Cite this

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AB - We show that if (X, T) is a topological dynamical system which is deterministic in the sense of Kamiński, Siemaszko and Szymański then (X, T -1) and (X × X, T × T) need not be deterministic in this sense. However if (X × X, T × T) is deterministic then (X, T n) is deterministic for all n ∈ ℕ \ {0}.

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KW - Topological dynamics

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Inverses, powers and cartesian products of topologically deterministic maps

Abstract

Keywords

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