Artykuł w czasopiśmie
Brak miniatury
Licencja
ClosedAccessDostęp zamknięty
 

Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra

Uproszczony widok
cris.lastimport.scopus2024-02-12T19:41:19Z
dc.abstract.enThe formalism for Poisson–Hopf (PH) deformations of Lie–Hamilton (LH) systems, recently proposed in Ballesteros Á et al (2018 J. Phys. A: Math. Theor. 51 065202), is refined in one of its crucial points concerning applications, namely the obtention of effective and computationally feasible PH deformed superposition rules for prolonged PH deformations of LH systems. The two new notions here proposed are a generalization of the standard superposition rules and the concept of diagonal prolongations for Lie systems, which are consistently recovered under the non-deformed limit. Using a technique from superintegrability theory, we obtain a maximal number of functionally independent constants of the motion for a generic prolonged PH deformation of a LH system, from which a simplified deformed superposition rule can be derived. As an application, explicit deformed superposition rules for prolonged PH deformations of LH systems based on the oscillator Lie algebra ${\mathfrak{h}}_{4}$ are computed. Moreover, by making use that the main structural properties of the book subalgebra ${\mathfrak{b}}_{2}$ of ${\mathfrak{h}}_{4}$ are preserved under the PH deformation, we consider prolonged PH deformations based on ${\mathfrak{b}}_{2}$ as restrictions of those for ${\mathfrak{h}}_{4}$-LH systems, thus allowing the study of prolonged PH deformations of the complex Bernoulli equations, for which both the constants of the motion and the deformed superposition rules are explicitly presented.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorHerranz, Francisco J
dc.contributor.authorAraujo, Javier De Lucas
dc.contributor.authorFernández-Saiz, Eduardo
dc.contributor.authorCampoamor-Stursberg, Rutwig
dc.contributor.authorBallesteros, Angel
dc.date.accessioned2024-01-25T17:00:08Z
dc.date.available2024-01-25T17:00:08Z
dc.date.issued2021
dc.description.financePublikacja bezkosztowa
dc.description.number20
dc.description.volume54
dc.identifier.doi10.1088/1751-8121/ABF1DB
dc.identifier.issn1751-8113
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/116169
dc.identifier.weblinkhttps://iopscience.iop.org/article/10.1088/1751-8121/abf1db
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.pages205202
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titlePoisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
dc.typeJournalArticle
dspace.entity.typePublication