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August  2013, 33(8): 3277-3287. doi: 10.3934/dcds.2013.33.3277

Toeplitz kneading sequences and adding machines

Lori Alvin 1,

1. 

Department of Mathematics and Statistics, University of West Florida, 11000 University Parkway, Pensacola, FL 32514, United States

Received  May 2012 Revised  November 2012 Published  January 2013

In this paper we provide a characterization for a shift maximal sequence of 1's and 0's to be the kneading sequence for a unimodal map $f$ with $f|_{\omega(c)}$ topologically conjugate to an adding machine, where $c$ is the turning point of $f$. We show that the unimodal map $f$ has an embedded adding machine if and only if $\mathcal{K}(f)$ is a one-sided, non-periodic Toeplitz sequence with the finite time containment property. We then show the existence of unimodal maps with Toeplitz kneading sequences that do not have the finite time containment property.
Keywords: Adding machines, Toeplitz sequences, kneading sequences, unimodal maps..
Mathematics Subject Classification: Primary: 54H20, 37B10; Secondary: 37E0.
Citation: Lori Alvin. Toeplitz kneading sequences and adding machines. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3277-3287. doi: 10.3934/dcds.2013.33.3277
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show all references

References:
[1]

J. Difference Eq. and Appl., 18 (2012), 657-674. doi: 10.1080/10236198.2011.608066.  Google Scholar

[2]

Fund. Math., 209 (2010), 81-93. doi: 10.4064/fm209-1-6.  Google Scholar

[3]

J. Math. Anal. Appl., 115 (1986), 305-362 doi: 10.1016/0022-247X(86)90001-6.  Google Scholar

[4]

Topology Appl., 140 (2004), 151-161. doi: 10.1016/j.topol.2003.07.006.  Google Scholar

[5]

Ergod. Th. & Dynam. Sys., 26 (2006), 673-682 . doi: 10.1017/S0143385705000635.  Google Scholar

[6]

Cambridge University Press, 2004.  Google Scholar

[7]

Birkhauser, 1980.  Google Scholar

[8]

Commun. Math. Phys., 127 (1990), 319-337.  Google Scholar

[9]

Topology Appl., 156 (2009), 2735-2746. doi: 10.1016/j.topol.2008.11.018.  Google Scholar

[10]

Springer Verlag, 1993.  Google Scholar

[11]

Z. Wahrsch. Verw. Gebiete, 67 (1984), 95-107. doi: 10.1007/BF00534085.  Google Scholar

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