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  • A transitive homeomorphism on the Lelek fan
    Banič, Iztok ; Erceg, Goran ; Kennedy, Judy A.
    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.
    Source: Journal of difference equations and applications. - ISSN 1023-6198 (Vol. 29, no. 4, 2023, str. 393-418)
    Type of material - article, component part ; adult, serious
    Publish date - 2023
    Language - english
    COBISS.SI-ID - 151598851

    Link(s):

    Digital Library of the University of Maribor – DLUM

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