The Dynamical System Generated by the Floor Function λx - Rozikov, U.A.; Sattarov, I.A.; Usmonov, J.B. (Journal of Applied Nonlinear Dynamics, 2026)
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.