Article in Journal ART-2012-05

BibliographyFutter, Ben; Avrutin, Viktor; Schanz, Michael: The discontinuous flat top tent map and the nested period incrementing bifurcation structure.
In: Chaos, Solitons & Fractals. Vol. 45(4).
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 465-482, english.
Elsevier, April 2012.
DOI: 10.1016/j.chaos.2012.01.009; ISSN: 0960-0779.
Article in Journal.
CR-SchemaG.2.0 (Discrete Mathematics General)
J.2 (Physical Sciences and Engineering)
Keywordsdiscontinuous flat top tent map; nested period incrementing; symbolic dynamics; U-sequence; discontinuous maps
Abstract

In this work we report the recently discovered nested period incrementing bifurcation scenario. The investigated piecewise linear map is defined on three partitions of the unit interval, constant in the middle partition and therefore displays a rich variety of superstable orbits. These orbits are arranged according to an infinite binary tree of the corresponding symbolic sequences, which can be generated by a simple set of rules. The system also allows for straightforward computation of the respective regions of existence. One of the most striking results of our investigations is that the famous U-sequence is inevitably embedded in the nested period incrementing scenario.

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Copyright© 2012 Elsevier
Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
Entry dateFebruary 24, 2012
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