About: The Zermelo conditions and higher order homogeneous functions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Invariance under reparametrizations of integral curves of higher order di?erential equations, including variational equations related to Finsler geometry, is studied. The classical homogeneity concepts are introduced within the theory of (jet) differential groups, known in the theory of differential invariants. On this basis the well-known generalizations of the Euler theorem are obtained (the Zermelo conditions). It is shown that every integral curve of a system of differential equations whose left-hand sides are higher order positive homogeneous functions, is invariant with respect to all reparametrizations, i.e. a set solution. Then the positive homogeneity concept is applied to second order variational equations. We show that the systems with positive homogeneous Lagrangians are de?ned by positive homogeneous functions, and vice versa. Invariance under reparametrizations of integral curves of higher order di?erential equations, including variational equations related to Finsler geometry, is studied. The classical homogeneity concepts are introduced within the theory of (jet) differential groups, known in the theory of differential invariants. On this basis the well-known generalizations of the Euler theorem are obtained (the Zermelo conditions). It is shown that every integral curve of a system of differential equations whose left-hand sides are higher order positive homogeneous functions, is invariant with respect to all reparametrizations, i.e. a set solution. Then the positive homogeneity concept is applied to second order variational equations. We show that the systems with positive homogeneous Lagrangians are de?ned by positive homogeneous functions, and vice versa. (en)
Title	The Zermelo conditions and higher order homogeneous functions The Zermelo conditions and higher order homogeneous functions (en)
skos:prefLabel	The Zermelo conditions and higher order homogeneous functions The Zermelo conditions and higher order homogeneous functions (en)
skos:notation	RIV/61988987:17310/13:A1401A5E!RIV14-GA0-17310___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(EE2.3.30.0058), P(GA201/09/0981)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Krupka, Demeter
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	Ostravská univerzita v Ostravě / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	118691
http://linked.open...ai/riv/idVysledku	RIV/61988987:17310/13:A1401A5E
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	homogeneous function; Zermelo conditions; Euler's theorem; MultiSet solutions; jet; differential group (en)
http://linked.open.../riv/klicoveSlovo	differential group jet homogeneous function Euler's theorem MultiSet solutions Zermelo conditions
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[3475D0BBA2E2]
http://linked.open...i/riv/nazevZdroje	PUBL MATH-DEBRECEN
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Global Analysis and the Geometry of Fibred Spaces Development of Research Teams at the University of Pardubice
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	82
http://linked.open...iv/tvurceVysledku	Krupka, Demeter Urban, Z.
issn	0033-3883
number of pages	17 (xsd:int)
http://localhost/t...ganizacniJednotka	17310

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