关于亨农映射汇点的存在区域结构

On the structure of existence regions for sinks of the Hénon map.

作者信息

Galias Zbigniew, Tucker Warwick

机构信息

Department of Electrical Engineering, AGH University of Science and Technology, al. Mickiewicza 30, Kraków 30-059, Poland.

Department of Mathematics, Uppsala University, Box 480, Uppsala 751 06, Sweden.

出版信息

Chaos. 2014 Mar;24(1):013120. doi: 10.1063/1.4865110.

DOI:10.1063/1.4865110

PMID:24697382

Abstract

An extensive search for stable periodic orbits (sinks) for the Hénon map in a small neighborhood of the classical parameter values is carried out. Several parameter values which generate a sink are found and verified by rigorous numerical computations. Each found parameter value is extended to a larger region of existence using a simplex continuation method. The structure of these regions of existence is investigated. This study shows that for the Hénon map, there exist sinks close to the classical case.

摘要

在经典参数值的小邻域内对Hénon映射的稳定周期轨道（汇）进行了广泛搜索。通过严格的数值计算找到了几个产生汇的参数值并进行了验证。使用单纯形延拓方法将每个找到的参数值扩展到更大的存在区域。研究了这些存在区域的结构。这项研究表明，对于Hénon映射，在经典情况附近存在汇。