Inverses, powers and cartesian products of topologically deterministic maps

Michael Hochman; Artur Siemaszko

Inverses, powers and cartesian products of topologically deterministic maps

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

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

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Cite this

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abstract = "We show that if (X, T) is a topological dynamical system which is deterministic in the sense of Kami{\'n}ski, Siemaszko and Szyma{\'n}ski 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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AU - Hochman, Michael

AU - Siemaszko, Artur

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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}.

KW - Recurrence

KW - Topological determinism

KW - Topological dynamics

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M3 - مقالة

SN - 1230-3429

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JO - Topological Methods in Nonlinear Analysis

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IS - 1

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Inverses, powers and cartesian products of topologically deterministic maps

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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