Abstract:
The action of the pseudogroup of point transformations on the set of smooth functions on the contact 1-jet space J1R is considered. Differential invariants of this action are found, and the problem of local point equivalence of regular smooth functions is solved.
Keywords:
jet space, point pseudogroup, differential invariant, invariant derivation.
Citation:
P. V. Bibikov, “Point Equivalence of Functions on the 1-Jet Space J1R”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 19–25; Funct. Anal. Appl., 48:4 (2014), 250–255
\Bibitem{Bib14}
\by P.~V.~Bibikov
\paper Point Equivalence of Functions on the $1$-Jet Space $J^1\mathbb{R}$
\jour Funktsional. Anal. i Prilozhen.
\yr 2014
\vol 48
\issue 4
\pages 19--25
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\jour Funct. Anal. Appl.
\yr 2014
\vol 48
\issue 4
\pages 250--255
\crossref{https://doi.org/10.1007/s10688-014-0068-6}
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Linking options:
https://www.mathnet.ru/eng/faa3167
https://doi.org/10.4213/faa3167
https://www.mathnet.ru/eng/faa/v48/i4/p19
This publication is cited in the following 5 articles:
P. Bibikov, A. Malakhov, “On classification problems in the theory of differential equations: Algebra + geometry”, Publ. Inst. Math.-Beograd, 103:117 (2018), 33–52
P. V. Bibikov, “On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y''=A(x,y)y'+B(x,y)$”, Math. Notes, 104:2 (2018), 167–175
P. V. Bibikov, “On Lie's problem and differential invariants of ODEs $y''=F(x,y)$”, Funct. Anal. Appl., 51:4 (2017), 255–262
P. V. Bibikov, “Generalized Lie problem and differential invariants for the third order ODEs”, Lobachevskii J. Math., 38:4, SI (2017), 622–629
Pavel Bibikov, “On symplectization of 1-jet space and differential invariants of point pseudogroup”, Journal of Geometry and Physics, 85 (2014), 81
Citation in format AMSBIB
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