Abstract
The action of the pseudogroup of point transformations on the set of smooth functions on the contact 1-jet space J 1ℝ is considered. Differential invariants of this action are found, and the problem of local point equivalence of regular smooth functions is solved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. V. Alekseevskii, A. M. Vinogradov, and V. V. Lychagin, Main Ideas and Notions of Differential Geometry [in Russian], Geometry-1, Itogi Nauki i tekhniki. Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya, vol. 28, VINITI, Moscow, 1988.
V. I. Arnold, Geometric Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York-Berlin-Heidelberg, 1996.
B. S. Kruglikov and V. V. Lychagin, Global Lie-Tresse theorem, http://arxiv.org/abs/1111.5480v1.
V. V. Lychagin, “Feedback differential invariants,” Acta Appl. Math., 109:1 (2010), 211–222.
B. S. Kruglikov, “Point classification of Second Order ODEs: Tresse Classification Revisited and Beyond,” in: Proc. of the Fifth Abel Symposium (Tromso, Norway, June 17–22), Springer-Verlag, Berline-Heidelberg, 2009; http://arxiv.org/abs/0809.4653.
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 4, pp. 19–25, 2014
Original Russian Text Copyright © by P. V. Bibikov
Rights and permissions
About this article
Cite this article
Bibikov, P.V. Point equivalence of functions on the 1-jet space J 1ℝ. Funct Anal Its Appl 48, 250–255 (2014). https://doi.org/10.1007/s10688-014-0068-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10688-014-0068-6