Homogeneity and projective equivalence of differential equation fields

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F12%3AA13016A7" target="_blank" >RIV/61988987:17310/12:A13016A7 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Homogeneity and projective equivalence of differential equation fields

Original language description

We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are regular (in a natural sense that we define) form a projective equivalence class of homogeneous systems. We show further that the geodesics, or base integral curves, of projectively equivalent homogeneous differential equation fields are the same apart from orientation-preserving reparametrization; that is, homogeneous differential equation fields determine systems of paths.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F09%2F0981" target="_blank" >GA201/09/0981: Global Analysis and the Geometry of Fibred Spaces</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2012

Confidentiality

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

Name of the periodical

J. Geom. Mech.

ISSN

1941-4889

e-ISSN

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Volume of the periodical

4

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

21

Pages from-to

27-47

UT code for WoS article

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EID of the result in the Scopus database

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