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Description
  • Práce je věnována teorii lokálních variačních principů na fibrovaných prostorech, založené na pojmu lokálně variační diferenciální formy. Libovolné dvě Lepageovy formy, které definují lokální varnační princip pro tuto formu, splňují obdobné podmínky jako známé variační funkcionály Chernova-Simonsova typu. Vznikající teorie rozšiřuje teorii Lagrangeových - Souriauových forme prvního řádu, předloženou Grigorem, a uzavřených ekvivalentů Eulerových - Lagrangeových rovnic prvního řádu podle Hakové a Krupkové. Koncepčně se předkládaná teorie liší od přístupu k dané problematice na bázi Poincaré - Cartanových forem, publikovaného Prietem. (cs)
  • We present the theory of higher order local variational principles in fibered manifolds, in which the fundamental global concept is a locally variational dynamical form. Any two Lepage forms, defining a local variational principle for this form, differ on intersection of their domains by a variationally trivial form. In this sense, but in a different geometric setting, the local variational principles satisfy analogous properties as the variational functionals of the Chern-Simons type. The resulting theory of extremals and symmetries extends the first order theories of the Lagrange/Souriau form, presented by Grigore and Popp, and closed equivalents of the first order Euler-Lagrange forms of Hakova and Krupkova. Conceptually, our approach differs from Prieto, who uses the Poincare-Cartan forms, which do not have higher order global analogues.
  • We present the theory of higher order local variational principles in fibered manifolds, in which the fundamental global concept is a locally variational dynamical form. Any two Lepage forms, defining a local variational principle for this form, differ on intersection of their domains by a variationally trivial form. In this sense, but in a different geometric setting, the local variational principles satisfy analogous properties as the variational functionals of the Chern-Simons type. The resulting theory of extremals and symmetries extends the first order theories of the Lagrange/Souriau form, presented by Grigore and Popp, and closed equivalents of the first order Euler-Lagrange forms of Hakova and Krupkova. Conceptually, our approach differs from Prieto, who uses the Poincare-Cartan forms, which do not have higher order global analogues. (en)
Title
  • Variational principles for locally variational forms
  • Variační principy pro lokálně variační formy (cs)
  • Variational principles for locally variational forms (en)
skos:prefLabel
  • Variational principles for locally variational forms
  • Variační principy pro lokálně variační formy (cs)
  • Variational principles for locally variational forms (en)
skos:notation
  • RIV/61989592:15310/05:00001808!RIV06-MSM-15310___
http://linked.open.../vavai/riv/strany
  • 1-15
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/0512), Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika
  • 5
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 548535
http://linked.open...ai/riv/idVysledku
  • RIV/61989592:15310/05:00001808
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • fibered manifolds; higher order local variational principles (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [884186B064A1]
http://linked.open...i/riv/nazevZdroje
  • Journal of Mathematical Physics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 46
http://linked.open...iv/tvurceVysledku
  • Krupka, Demeter
  • Brajerčík, J.
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-2488
number of pages
http://localhost/t...ganizacniJednotka
  • 15310
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