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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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The Dynamical System Generated by the Floor Function λx

Journal of Applied Nonlinear Dynamics 5(2) (2016) 185--191 | DOI:10.5890/JAND.2016.06.005

U.A. Rozikov; I.A. Sattarov; J.B. Usmonov

Institute of Mathematics, 29, Do’rmon Yo’li str., 100125, Tashkent, Uzbekistan Namangan State University, Namangan, Uzbekistan

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We investigate the dynamical system generated by the floor function λx defined on R and with a parameter λ ∈ R. For each given m ∈ N we show that there exists a region of values of λ, where the floor function has exactly m fixed points (which are non-negative integers), also there is another region for λ , where there are exactly m+1 fixed points (which are non-positive integers). Moreover the full set Z of integer numbers is the set of fixed points iff λ = 1. We show that depending on λ and on the initial point x the limit of the forward orbit of the dynamical system may be one of the following possibilities: (i) a fixed point, (ii) a two-periodic orbit or (iii) ±ꝏ.


U.Rozikov thanks Aix-Marseille University Institute for Advanced Study IMéRA (Marseille, France) for support by a residency scheme. His work also partially supported by the Grant No.0251/GF3 of Education and Science Ministry of Republic of Kazakhstan.


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