Higher-order differential represented by connections on prolongations of a fibered manifold

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F00%3A00000034" target="_blank" >RIV/47813059:19610/00:00000034 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Higher-order differential represented by connections on prolongations of a fibered manifold

Popis výsledku v původním jazyce

This long survey paper represents an introduction to a recently developed formalism which is aimed primarily at a systematic description of certain phenomena related to the geometry of systems of differential equations in normal form. These equations arerepresented by connections on prolongations of a fibered manifold. We recalls some notions and results about jet prolongations of sections, morphisms and vector fields, total derivatives, the contact structure and the Cartan distribution on $Jsp kpi$,repeated jets and higher-order connections on $pi$. Then the integrability, the prolongations, reductions and symmetries of higher-order differential equations are studied. Some integration methods of fields of paths are discussed. In fact,since the higher-order connections may be composed with suitable morphisms, they may be viewed as the integral sections of some other connections. Finally, semispray connections are studied.

Název v anglickém jazyce

Higher-order differential represented by connections on prolongations of a fibered manifold

Popis výsledku anglicky

This long survey paper represents an introduction to a recently developed formalism which is aimed primarily at a systematic description of certain phenomena related to the geometry of systems of differential equations in normal form. These equations arerepresented by connections on prolongations of a fibered manifold. We recalls some notions and results about jet prolongations of sections, morphisms and vector fields, total derivatives, the contact structure and the Cartan distribution on $Jsp kpi$,repeated jets and higher-order connections on $pi$. Then the integrability, the prolongations, reductions and symmetries of higher-order differential equations are studied. Some integration methods of fields of paths are discussed. In fact,since the higher-order connections may be composed with suitable morphisms, they may be viewed as the integral sections of some other connections. Finally, semispray connections are studied.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA201%2F97%2F0001" target="_blank" >GA201/97/0001: Dynamické systémy</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2000

Kód důvěrnosti údajů

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

Název periodika

Extracta Mathematicae

ISSN

ISSN0213-8743

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

92

Strana od-do

421-512

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—