Dynamical systems and Poisson structures
dc.authorid | Zheltukhin, Kostyantyn/0000-0002-1098-7369 | |
dc.authorid | Gurses, Metin/0000-0002-3439-3952 | |
dc.authorscopusid | 7003662154 | |
dc.authorscopusid | 25026129500 | |
dc.authorscopusid | 6603497099 | |
dc.authorwosid | , Metin/T-3710-2019 | |
dc.authorwosid | Zheltukhin, Kostyantyn/AAZ-6715-2020 | |
dc.contributor.author | Hüseyin, Hüseyin Şirin | |
dc.contributor.author | Guseinov, Gusein Sh | |
dc.contributor.author | Zheltukhin, Kostyantyn | |
dc.contributor.other | Mathematics | |
dc.date.accessioned | 2024-07-05T15:12:03Z | |
dc.date.available | 2024-07-05T15:12:03Z | |
dc.date.issued | 2009 | |
dc.department | Atılım University | en_US |
dc.department-temp | [Guerses, Metin] Bilkent Univ, Fac Sci, Dept Math, TR-06800 Ankara, Turkey; [Guseinov, Gusein Sh] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey; [Zheltukhin, Kostyantyn] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey | en_US |
dc.description | Zheltukhin, Kostyantyn/0000-0002-1098-7369; Gurses, Metin/0000-0002-3439-3952 | en_US |
dc.description.abstract | We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919] | en_US |
dc.description.sponsorship | Turkish Academy of Sciences; Scientific and Technical Research Council of Turkey | en_US |
dc.description.sponsorship | wish to thank Professor M. Blaszak for critical reading of the paper and for constructive comments. This work is partially supported by the Turkish Academy of Sciences and by the Scientific and Technical Research Council of Turkey. | en_US |
dc.identifier.citation | 16 | |
dc.identifier.doi | 10.1063/1.3257919 | |
dc.identifier.issn | 0022-2488 | |
dc.identifier.issn | 1089-7658 | |
dc.identifier.issue | 11 | en_US |
dc.identifier.scopus | 2-s2.0-72249092277 | |
dc.identifier.uri | https://doi.org/10.1063/1.3257919 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14411/1530 | |
dc.identifier.volume | 50 | en_US |
dc.identifier.wos | WOS:000272755100015 | |
dc.identifier.wosquality | Q3 | |
dc.language.iso | en | en_US |
dc.publisher | Amer inst Physics | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | [No Keyword Available] | en_US |
dc.title | Dynamical systems and Poisson structures | en_US |
dc.type | Article | en_US |
dspace.entity.type | Publication | |
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