About: A simple way of making a Hamiltonian system into a bi-Hamiltonian one

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Pro danou Poissonovu strukturu (nebo, ekvivalentně, Hamiltonův operátor) $P$ dokazujeme, že jeho Lieova derivace $L_{\tau} (P )$ podél vektorového pole $\tau$ zase je Poissonovou strukturou, která je automaticky kompatibilní s $P$, tehdy a jen tehdy, pokud $[L^2_{\tau} (P ), P] = 0$, kde $[\cdot, \cdot]$ je Schoutenova závorka. Tento výsledek vede k novému lokálnímu popisu množiny všech Poissonových struktur, kompatibilních s danou Poissonovou strukturou $P$ lokálně stálého rangu takovou, že $\dim\ker P\leq 1$, a zároveň vede k pozoruhodně jednoduché konstrukci bihamiltonových dynamických systémů. Rovněž uveden nový popis dvojic kompatibilních lokálních Hamiltonových operátorů Dubrovinova--Novikovova typu. (cs) Given a Poisson structure (or, equivalently, a Hamiltonian operator) $P$, we show that its Lie derivative $L_{\tau}(P)$ along a vector field $\tau$ defines another Poisson structure, which is automatically compatible with $P$, if and only if $[L_{\tau}^2(P),P]=0$, where $[\cdot,\cdot]$ is the Schouten bracket. This result yields a new local description for the set of all Poisson structures compatible with a given Poisson structure $P$ of locally constant rank such that $\dim\ker P\leq 1$ and leads to a remarkably simple construction of bi-Hamiltonian dynamical systems. A new description for pairs of compatible local Hamiltonian operators of Dubrovin?Novikov type is also presented. Given a Poisson structure (or, equivalently, a Hamiltonian operator) $P$, we show that its Lie derivative $L_{\tau}(P)$ along a vector field $\tau$ defines another Poisson structure, which is automatically compatible with $P$, if and only if $[L_{\tau}^2(P),P]=0$, where $[\cdot,\cdot]$ is the Schouten bracket. This result yields a new local description for the set of all Poisson structures compatible with a given Poisson structure $P$ of locally constant rank such that $\dim\ker P\leq 1$ and leads to a remarkably simple construction of bi-Hamiltonian dynamical systems. A new description for pairs of compatible local Hamiltonian operators of Dubrovin?Novikov type is also presented. (en)
Title	Jednoduchý způsob jak udělat z Hamiltonova systému bihamiltonův (cs) A simple way of making a Hamiltonian system into a bi-Hamiltonian one A simple way of making a Hamiltonian system into a bi-Hamiltonian one (en)
skos:prefLabel	Jednoduchý způsob jak udělat z Hamiltonova systému bihamiltonův (cs) A simple way of making a Hamiltonian system into a bi-Hamiltonian one A simple way of making a Hamiltonian system into a bi-Hamiltonian one (en)
skos:notation	RIV/47813059:19610/04:00011724!RIV/2005/GA0/196105/N
http://linked.open.../vavai/riv/strany	183;197
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/00/0724), Z(MSM 192400002)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2005
http://linked.open...aciTvurceVysledku	Sergyeyev, Artur
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	553184
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/04:00011724
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	compatible Poisson structures; Hamiltonian operators; bi-Hamiltonian systems; integrability; Schouten bracket; master symmetry; Lichnerowicz;Poisson cohomology; hydrodynamic type systems (en)
http://linked.open.../riv/klicoveSlovo	Hamiltonian operators Lichnerowicz Schouten bracket bi-Hamiltonian systems hydrodynamic type systems integrability master symmetry Poisson cohomology compatible Poisson structures
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[BA982492D47A]
http://linked.open...i/riv/nazevZdroje	Acta Applicandae Mathematicae
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Geometric analysis
http://linked.open...UplatneniVysledku	2004
http://linked.open...v/svazekPeriodika	83
http://linked.open...iv/tvurceVysledku	Sergyeyev, Artur
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20192400002
issn	0167-8019
number of pages	15 (xsd:int)
http://localhost/t...ganizacniJednotka	19610

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