Original scientific paper

https://doi.org/10.3336/gm.59.2.10

Minimal dynamical systems with closed relations

Iztok Banič ; Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia, Andrej Marušič Institute, University of Primorska, Muzejski trg 2, SI-6000 Koper, Slovenia
Goran Erceg ; Faculty of Science, University of Split, Rudera Boškovića 33, Split, Croatia
Rene Gril Rogina ; Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia
Judy Kennedy ; Lamar University, 200 Lucas Building, P.O. Box 10047, Beaumont, TX 77710, USA

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Abstract

We introduce dynamical systems \((X,G)\) with closed relations \(G\) on compact metric spaces \(X\) and discuss different types of minimality of such dynamical systems, all of them generalizing minimal dynamical systems \((X,f)\) with continuous function \(f\) on a compact metric space \(X\).

Keywords

Closed relations, dynamical systems, minimal dynamical systems, \(CR\)-dynamical systems, minimal \(CR\)-dynamical systems, backward minimal \(CR\)-dynamical systems, invariant sets, forward orbits, backward orbits, omega limit sets, alpha limit sets, topological conjugations

Hrčak ID:

325179

URI

https://hrcak.srce.hr/325179

Publication date:

26.12.2024.

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