On a strong dense periodicity property of shifts of finite type

Journal Article · Thu Oct 22 00:00:00 EDT 2015 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4932491· OSTI ID:22492503

Dzul-Kifli, Syahida Che; Al-Muttairi, Hassan ^[1]

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1. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (Malaysia)

There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ{sub 2}, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive.

• OSTI ID: 22492503
• Journal Information: AIP Conference Proceedings, Vol. 1682, Issue 1; Conference: SKSM22: 22. National symposium on mathematical sciences - Strengthening research and collaboration of mathematical sciences in Malaysia, Selangor (Malaysia), 24-26 Nov 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
DENSITY
PERIODICITY
SENSITIVITY