WHAT MAPS CAN ADMIT TWO-SIDED SYMBOLIC DYNAMICAL SYSTEMS?
2005 ◽
Vol 15
(04)
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pp. 1485-1491
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A continuous map f from a metric space X to itself is said to contain a two-sided symbolic dynamical system if there exists an invariant set X0 of f such that the subsystem f|X0 is topologically conjugate to the shift map on a two-sided sequence space of some symbols. In this paper we show that, for any given integer n ≥ 2, there exists a Lipschitz continuous interval map which contains a two-sided symbolic dynamical system of n symbols. Furthermore, we investigate the effect of differentiability and monotonicity assumptions, and prove that neither piecewise monotonic nor piecewise continuously differentiable graph map can contain a two-sided symbolic dynamical system.
2017 ◽
Vol 39
(3)
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pp. 604-619
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2012 ◽
Vol 204-208
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pp. 4776-4779
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1993 ◽
Vol 13
(1)
◽
pp. 1-5
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2015 ◽
Vol 25
(09)
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pp. 1550115
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2018 ◽
Vol 32
(15)
◽
pp. 1850166
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2014 ◽
Vol 2014
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pp. 1-4
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Keyword(s):
2016 ◽
Vol 30
(02)
◽
pp. 1550274
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