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Communications in Mathematical Physics
Article . 2000 . Peer-reviewed
License: Springer TDM
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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The Generalized Milnor–Thurston Conjecture and Equal Topological Entropy Class in Symbolic Dynamics of Order Topological Space of Three Letters

The generalized Milnor-Thurston conjecture and equal topological entropy class in symbolic dynamics of order topological space of three letters
Authors: Peng, Shouli; Zhang, Xusheng;

The Generalized Milnor–Thurston Conjecture and Equal Topological Entropy Class in Symbolic Dynamics of Order Topological Space of Three Letters

Abstract

Write \(\mathcal U=\{L,C,M,D,R\}\), when \({\mathcal U}^\infty\) is the set of infinite sequences of the symbols \(LB_k\) [if \((A_0,A_1,\ldots,A_{k-1})\) has an odd number of \(M\)'s]. Let \(\varphi: {\mathcal U}^\infty\rightarrow {\mathcal U}^\infty\) be the \textit{shift map}, that is, \(\varphi(A_0,A_1,\ldots)=(A_1,A_2,\ldots)\). We will say that two sequences \(K^1, K^2\in {\mathcal U}^\infty\) are \textit{admissible} if they satisfy the following conditions for any \(r\in \{1,2\}\): (a) if \(K^r=(A_0,A_1,\ldots ,A_k,\ldots)\) and \(A_k\) equals \(C\) (resp. \(D\)), then \(\varphi^k(K^r)=K^1\) [resp. \(\varphi^k(K^r)=K^2\)]; (b) \(K^1 \preceq \varphi^i(K^r)\preceq K^2\) for any positive integer \(i\). We call the set \(\Sigma_3\) of admissible pairs \((K^1, K^2)\) the \textit{kneading plane}. The reason is that if \(f\) is a \textit{boundary anchored bimodal map with the shape \((+,-,+)\)}, that is, a continuous map \(f:[a,b]\rightarrow [a,b]\) with \(f(a)=a\), \(f(b)=b\) such that, for some intermediate points \(a

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Keywords

Dynamical systems involving maps of the interval, Topological entropy, symbolic dynamics, bimodal map, topological entropy, Entropy in general topology, Symbolic dynamics, Topological dynamics, \(*\)-product, kneading plane

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
11
Average
Top 10%
Average
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