A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles

Hidetaka ITO  Hiroomi HIKAWA  Yutaka MAEDA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.7   pp.1127-1131
Publication Date: 2018/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1127
Type of Manuscript: LETTER
Category: Nonlinear Problems
Keyword: 
chaotic saddles,  unstable periodic orbits,  bifurcation,  Newton iteration,  subspace method,  

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Summary: 
This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.