Aitu N.2025-08-112025-08-112020Aitu N / Cardinality of survivor sets in open dynamical systems / 6M060100 - Department of Natural sciences / 2020https://repository.sdu.edu.kz/handle/123456789/1853In this thesis, our goal is to learn about open dynamical systems corresponding interval maps. We study the class of dynamical systems with holes: Expanding maps of the interval. In detail, We consider symbolic dynamics with holes. Let H-hole lies in the interval [0, 1) and let T : [0, 1) −→ [0, 1) be a self map. The survivor set Ω(H) := {x ∈ [0, 1) : T nx /∈ H, n ≥ 0}. Depending on location and size of the holes we will characterize and study the survivor set Ω(H) infinite or finite, uncountable or countable and survivor set Ω(H) has positive entropy.enChaos theorySymbolic dynamicsProof of main resultsThesis