Rigorous and accurate enclosure of invariant manifolds on surfaces
Rigorous and accurate enclosure of invariant manifolds on surfaces
Knowledge about stable and unstable manifolds of hyperbolic fixed points of certain maps is desirable in many fields of research, both in pure mathematics as well as in applications, ranging from forced oscillations to celestial mechanics and space mission design. We present a technique to find highly accurate polynomial approximations of local invariant manifolds for sufficiently smooth planar maps and rigorously enclose them with sharp interval remainder bounds using Taylor model techniques. Iteratively, significant portions of the global manifold tangle can be enclosed with high accuracy. Numerical examples are provided.
Homoclinic point, Hyperbolicity, Invariant manifold, Taylor model
107-126
Wittig, A.
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Berz, M.
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Grote, J.
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Makino, K.
833360d9-db7d-42ac-b184-98c31b0c9fe0
Newhouse, S.
ff887994-aa73-443f-93a4-9aa72923d29c
June 2010
Wittig, A.
3a140128-b118-4b8c-9856-a0d4f390b201
Berz, M.
95c4e8a8-e1d9-4ad7-91c6-2832b7a1dd02
Grote, J.
b6f060be-cec8-4427-a92e-6a5a50fa1dcb
Makino, K.
833360d9-db7d-42ac-b184-98c31b0c9fe0
Newhouse, S.
ff887994-aa73-443f-93a4-9aa72923d29c
Wittig, A., Berz, M., Grote, J., Makino, K. and Newhouse, S.
(2010)
Rigorous and accurate enclosure of invariant manifolds on surfaces.
Regular and Chaotic Dynamics, 15 (2), .
(doi:10.1134/S1560354710020024).
Abstract
Knowledge about stable and unstable manifolds of hyperbolic fixed points of certain maps is desirable in many fields of research, both in pure mathematics as well as in applications, ranging from forced oscillations to celestial mechanics and space mission design. We present a technique to find highly accurate polynomial approximations of local invariant manifolds for sufficiently smooth planar maps and rigorously enclose them with sharp interval remainder bounds using Taylor model techniques. Iteratively, significant portions of the global manifold tangle can be enclosed with high accuracy. Numerical examples are provided.
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e-pub ahead of print date: 27 April 2010
Published date: June 2010
Keywords:
Homoclinic point, Hyperbolicity, Invariant manifold, Taylor model
Identifiers
Local EPrints ID: 419781
URI: http://eprints.soton.ac.uk/id/eprint/419781
ISSN: 1560-3547
PURE UUID: 80209645-4242-4cab-be8e-898ca1e9afa1
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Date deposited: 20 Apr 2018 16:30
Last modified: 16 Mar 2024 04:30
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Contributors
Author:
M. Berz
Author:
J. Grote
Author:
K. Makino
Author:
S. Newhouse
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