Computer assisted proof of chaos in the Rossler equations and in the Henon map

被引:110
作者
Zgliczynski, P
机构
[1] Jagiellonian University, Institute of Mathematics, 30-059 Krakow
关键词
D O I
10.1088/0951-7715/10/1/016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce horseshoe-type mappings which are geometrically similar to Smale's horseshoes. For such mappings we prove by means of the fixed point index the existence of chaotic dynamics-the semi-conjugacy to the shift on a finite number of symbols. Our theorem does not require any assumptions concerning derivatives, it is a purely topological result. The assumptions of our theorem are then rigorously verified by computer assisted computations for the classical Henon map and for classical Rossler equations.
引用
收藏
页码:243 / 252
页数:10
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