@article{article_1487804, title={A COUNTEREXAMPLE TO ELAYDI’S CONJECTURE}, journal={Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler}, volume={13}, pages={1–6}, year={2025}, DOI={10.20290/estubtdb.1487804}, author={Güvey, İsmail Alper}, keywords={Chaos, Topologically Transitive, Totally Transitive, Topological Conjugacy}, abstract={In 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.}, number={1}, publisher={Eskişehir Teknik Üniversitesi}