Alper, Güvey İsmail2025-07-212025-07-2120252667-419Xhttps://dx.doi.org/10.20290/estubtdb.1487804https://hdl.handle.net/20.500.12451/13405In this work, we define a chaotic map that contradicts Elaydi’s conjecture. Firstly, we present some important concepts used in this paper and define a continuous map f on [0,2], which is connected according to the usual topology on R. Moreover, we show that f is chaotic on [0,2] by using topological conjugacy with the ‘tent map’. Finally, we conclude that f^2=f∘f is not chaotic on [0,2]. In addition, this example also shows that topological transitivity does not imply total transitivity.eninfo:eu-repo/semantics/openAccessChaosTopologically TransitiveTotally TransitiveTopological ConjugacyArticle1311610.20290/estubtdb.1487804