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A construction of a large family of integrable symplectic birational maps Suris, Yuri
Description
We give a construction of completely integrable (2m)-dimesnional Hamiltonian systems with m cubic integrals in involution. Applying to the corresponding quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme, we arrive at birational (2m)-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on $R^{2m}$, and possess m independent integrals of motion, which are perturbations of the original integrals. Thus, these maps are completely integrable in the Liouville-Arnold sense. Moreover, under a suitable normalization of the original m-tuples of commuting vector fields, the m-tuples of maps commute and share the invariant symplectic structure and m integrals of motion.
Item Metadata
Title |
A construction of a large family of integrable symplectic birational maps
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-10-06T09:00
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Description |
We give a construction of completely integrable (2m)-dimesnional Hamiltonian systems with m cubic integrals in involution. Applying to the corresponding quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme, we arrive at birational (2m)-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on $R^{2m}$, and possess m independent integrals of motion, which are perturbations of the original integrals. Thus, these maps are completely integrable in the Liouville-Arnold sense. Moreover, under a suitable normalization of the original m-tuples of commuting vector fields, the m-tuples of maps commute and share the invariant symplectic structure and m integrals of motion.
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Extent |
43 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Technical University of Berlin
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Series | |
Date Available |
2017-04-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0343495
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International