Intra-orbit separation of dense orbits of dendrite maps

Taixiang Sun, Qiuli He and Hongjian Xi

Chaos, Solitons & Fractals, 2013, vol. 57, issue C, 89-92

Abstract: In this note, we will generalize the notion of separation index, which was introduced by Manjunath et al. (2006), to dendrite maps, and use the notion to characterize the intra-orbit separation for the orbits of continuous transitive dendrite maps. We will show: (i) For a dendrite map f, the separation index γ is greater than zero if and only if the set of fixed points of f is not an arc connected subspace. (ii) If the separation index γ of a dendrite map f is greater than zero, then for every 0<τ<γ and any pair of distinct points x and y on a dense orbit, {x,y} is a Li–Yorke pair of modulus τ.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:57:y:2013:i:c:p:89-92

DOI: 10.1016/j.chaos.2013.09.001

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