Variational Equations on Manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F09%3A00010555" target="_blank" >RIV/61989592:15310/09:00010555 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Variational Equations on Manifolds

Popis výsledku v původním jazyce

The chapter is an exposition of the present state of the geometric theory of differential equations on fibred manifolds that are variational, i.e., come as equations for extremals of (generally higher-order and multiple) variational integrals. The following topics are included: Lepage forms and the first variation formula; the variational sequence, local and global aspects; ordinary differential equations in jet bundles: classification problems, structure of solutions, properties of regular equations, symmetries and conservation laws, inverse problem of the calculus of variations; geometric integration methods for variational ordinary differential equations: Noether Theorem, Liouville Theorem, Hamilton-Jacobi Theorems; variational partial differentialequations: existence and construction of Lagrangians, Hamiltonian systems, regular variational problems, Hamilton-Jacobi equation and fields of extremals, symmetries and conserved currents.

Název v anglickém jazyce

Variational Equations on Manifolds

Popis výsledku anglicky

The chapter is an exposition of the present state of the geometric theory of differential equations on fibred manifolds that are variational, i.e., come as equations for extremals of (generally higher-order and multiple) variational integrals. The following topics are included: Lepage forms and the first variation formula; the variational sequence, local and global aspects; ordinary differential equations in jet bundles: classification problems, structure of solutions, properties of regular equations, symmetries and conservation laws, inverse problem of the calculus of variations; geometric integration methods for variational ordinary differential equations: Noether Theorem, Liouville Theorem, Hamilton-Jacobi Theorems; variational partial differentialequations: existence and construction of Lagrangians, Hamiltonian systems, regular variational problems, Hamilton-Jacobi equation and fields of extremals, symmetries and conserved currents.

Druh

C - Kapitola v odborné knize

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F09%2F0981" target="_blank" >GA201/09/0981: Globální analýza a geometrie fibrovaných prostorů</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Advances in Mathematics Research, Vol. 9

ISBN

978-1-60692-179-1

Počet stran výsledku

75

Strana od-do

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Počet stran knihy

354

Název nakladatele

Nova Science Publishers, USA

Místo vydání

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Kód UT WoS kapitoly

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