
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
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
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
| 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). | 11 | |
| 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. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
