FORMULAS FOR THE TOPOLOGICAL ENTROPY OF MULTIMODAL MAPS BASED ON MIN-MAX SYMBOLS

被引:5
作者
Amigo, Jose M. [1 ]
Gimenez, Angel [1 ]
机构
[1] Univ Miguel Hernandez, Ctr Invest Operat, Elche 03202, Alicante, Spain
来源
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2015年 / 20卷 / 10期
关键词
Topological entropy; multimodal maps; symbolic dynamics; min-max symbols; algorithms; ALGORITHM; INTERVAL;
D O I
10.3934/dcdsb.2015.20.3415
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a new formula for the topological entropy of a multimodal map f is derived, and some basic properties are studied. By a formula we mean an analytical expression leading to a numerical algorithm; by a multimodal map we mean a continuous interval self-map which is strictly monotonic in a finite number of subintervals. The main feature of this formula is that it involves the min-max symbols of f, which are closely related to its kneading symbols. This way we continue our pursuit of finding expressions for the topological entropy of continuous multimodal maps based on min-max symbols. As in previous cases, which will be also reviewed, the main geometrical ingredients of the new formula are the numbers of transversal crossings of the graph of f and its iterates with the so-called "critical lines". The theoretical and practical underpinnings are worked out with the family of logistic parabolas and numerical simulations.
引用
收藏
页码:3415 / 3434
页数:20
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