(2020 International Young Scholars Workshop, 2020) Aitu N.; Bayadilova G.
Abstract. The aim of this paper is to give an overview of the dynamics of one dimensionaldiscrete dynamical systems: Tent map family T_3, Doubling map E_2 and shift map σ are investigated. Let I-intervals(Holes) lie in the interval [0,1) and let E_2 be a Doubling map. The survivor set Ω(I) :={x∈[0,1) : E_nx /∈ I, n≥0}. Depending on location and size of the intervals we will characterize the survivor set Ω(I) infinite or finite. Also we will show conjugacy of some maps that used in this paper. By using conjugacy of functions we will show that the Survivor set is infinite or finite in another composition of maps. The Cantor sets Λ that occur as non-survivor sets for c >2 from Tent map family T_c.[1]