Attractors in Pattern Iterations of Flat Top Tent Maps

Luis Silva ()
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Luis Silva: CIMA and Department of Mathematics of ISEL-Higher Institute of Engineering of Lisbon, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal

Mathematics, 2023, vol. 11, issue 12, 1-13

Abstract: Flat-topped one-dimensional maps have been used in the control of chaos in one-dimensional dynamical systems. In these applications, this mechanism is known as simple limiter control. In this paper, we will consider the introduction of simple limiters u in the tent map, according to a time-dependent scheme defined by a binary sequence s , the iteration pattern. We will define local and Milnor attractors in this non-autonomous context and study the dependence of their existence and coexistence on the value of the limiter u and on the pattern s . Using symbolic dynamics, we will be able to characterize the families of pairs ( u , s ) for which these attractors exist and coexist, as well as fully describe them. We will observe that this non-autonomous context provides a richness of behaviors that are not possible in the autonomous case.

Keywords: non-autonomous dynamical systems; interval maps; attractors; symbolic dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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