IEICE TRANSACTIONS on Fundamentals
A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.7 pp.1127-1131
- Publication Date
- 2018/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.1127
- Type of Manuscript
- LETTER
- Category
- Nonlinear Problems
Authors
Hidetaka ITO
Kansai University
Hiroomi HIKAWA
Kansai University
Yutaka MAEDA
Kansai University
Keyword
Latest Issue
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Hidetaka ITO, Hiroomi HIKAWA, Yutaka MAEDA, "A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 7, pp. 1127-1131, July 2018, doi: 10.1587/transfun.E101.A.1127.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1127/_p
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@ARTICLE{e101-a_7_1127,
author={Hidetaka ITO, Hiroomi HIKAWA, Yutaka MAEDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles},
year={2018},
volume={E101-A},
number={7},
pages={1127-1131},
abstract={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.},
keywords={},
doi={10.1587/transfun.E101.A.1127},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - A Subspace Newton-Type Method for Approximating Transversely Repelling Chaotic Saddles
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1127
EP - 1131
AU - Hidetaka ITO
AU - Hiroomi HIKAWA
AU - Yutaka MAEDA
PY - 2018
DO - 10.1587/transfun.E101.A.1127
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2018
AB - 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.
ER -
English
