Cardinality of survival set for the chaotic Tent map with holes

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Date

2020

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Journal ISSN

Volume Title

Publisher

2020 International Young Scholars Workshop

Abstract

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]

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Keywords

dynamical systems, symbolic dynamics, interval maps, survivor sets, chaos, open systems, irregular sets, 2020 International Young Scholars Workshop, №9

Citation

Aitu N , Bayadilova G / Cardinality of survival set for the chaotic Tent map with holes / 2020 International Young Scholars Workshop