COMPUTING THE TOPOLOGICAL ENTROPY OF UNIMODAL MAPS

被引：9

作者：

Dilao, Rui ^{[1
]}

Amigo, Jose ^{[2
]}

机构：

[1] IST, Dept Phys, NonLinear Dynam Grp, P-1049001 Lisbon, Portugal

[2] Univ Miguel Hernandez, Ctr Invest Operat, Elche 03202, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 06期

关键词：

Topological entropy; interval maps; symbolic dynamics; CHAOS; INTERVAL; DYNAMICS;

D O I：

10.1142/S0218127412501520

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. For this family of maps, the kneading sequence does not determine the lap numbers. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy of maps with direct and reverse bifurcations.

引用

页数：14

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