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A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles
Hidetaka ITO Hiroomi HIKAWA Yutaka MAEDA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2018/07/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Nonlinear Problems
chaotic saddles, unstable periodic orbits, bifurcation, Newton iteration, subspace method,
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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.