Naslov
A transitive homeomorphism on the Lelek fan

Autori
Banič, Iztok ; Erceg, Goran ; Kennedy, Judy

Izvornik
Journal of Difference Equations and Applications (1023-6198) 29 (2023); 1-26

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Closed relations ; Mahavier products ; transitive dynamical systems ; transitive homeomorphisms ; fans ; Lelek fans

Sažetak
Let X be a continuum and let φ:X→X be a homeomorphism. To construct a dynamical system (X, φ) with interesting dynamical properties, the continuum X often needs to have some complicated topological structure. In this paper, we are interested in one such dynamical property: transitivity. By now, various examples of continua X have been constructed in such a way that the dynamical system (X, φ) is transitive. Mostly, they are examples of continua that are not path- connected, such as the pseudo-arc or the pseudo- circle, or they are examples of locally connected continua (and every locally connected continuum is path-connected), Sierpiński carpet is such an example. In this paper, we present an example of a dynamical system (X, φ), where φ is a homeomorphism on the continuum X and X is a path-connected but not locally connected continuum. We construct a transitive homeomorphism on the Lelek fan. As a by-product, a non-invertible transitive map on the Lelek fan is also constructed.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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