Geodesic
Point Equivalence of Functions on the $1$-Jet Space $J^1\mathbb{R}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 19-25.

Voir la notice de l'article provenant de la source Math-Net.Ru

The action of the pseudogroup of point transformations on the set of smooth functions on the contact $1$-jet space $J^1\mathbb{R}$ is considered. Differential invariants of this action are found, and the problem of local point equivalence of regular smooth functions is solved.
Mots-clés : jet space, point pseudogroup
Keywords: differential invariant, invariant derivation. 
@article{FAA_2014_48_4_a2,
     author = {P. V. Bibikov},
     title = {Point {Equivalence} of {Functions} on the $1${-Jet} {Space} $J^1\mathbb{R}$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {19--25},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a2/}
}
TY  - JOUR
AU  - P. V. Bibikov
TI  - Point Equivalence of Functions on the $1$-Jet Space $J^1\mathbb{R}$
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2014
SP  - 19
EP  - 25
VL  - 48
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a2/
LA  - ru
ID  - FAA_2014_48_4_a2
ER  - 
%0 Journal Article
%A P. V. Bibikov
%T Point Equivalence of Functions on the $1$-Jet Space $J^1\mathbb{R}$
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2014
%P 19-25
%V 48
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a2/
%G ru
%F FAA_2014_48_4_a2
P. V. Bibikov. Point Equivalence of Functions on the $1$-Jet Space $J^1\mathbb{R}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 19-25. http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a2/

[1] D. V. Alekseevskii, A. M. Vinogradov, V. V. Lychagin, “Osnovnye idei i ponyatiya differentsialnoi geometrii”, Geometriya-1, Itogi nauki i tekhniki. Sovremenennye problemy matematiki. Fundamentalnye napravleniya, 28, VINITI, M., 1988 | MR | Zbl

[2] V. I. Arnold, Geometricheskie metody v teorii obyknovennykh differentsialnykh uravnenii, MTsNMO, M., 2012

[3] B. S. Kruglikov, V. V. Lychagin, Global Lie–Tresse theorem, arXiv: 1111.5480v1

[4] V. V. Lychagin, “Feedback differential invariants”, Acta Appl. Math., 109:1 (2010), 211–222 | DOI | MR | Zbl

[5] B. S. Kruglikov, “Point classification of Second Order ODEs: Tresse Classification Revisited and Beyond”, Proc. of the Fifth Abel Symposium (Tromso, Norway, June 17–22), Springer-Verlag, Berline–Heidelberg, 2009 ; arXiv: 0809.4653 | MR