Geodesic
On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 130-135.

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

Necessary and sufficient conditions under which two Abel equations with coefficients depending on the control parameter are locally equivalent with respect to the same pseudogroup of feedback transformations are found and are formulated in terms of differential invariants.
Mots-clés : Abel equations
Keywords: differential invariants, feedback transformation, control parameter. 
@article{INTO_2018_148_a15,
     author = {V. V. Shurygin (Jr.)},
     title = {On the {Equivalence} of {First-Order} {Abel} {Equations} with {Coefficients} {Depending} on the {Control} {Parameter}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {130--135},
     publisher = {mathdoc},
     volume = {148},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_148_a15/}
}
TY  - JOUR
AU  - V. V. Shurygin (Jr.)
TI  - On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 130
EP  - 135
VL  - 148
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_148_a15/
LA  - ru
ID  - INTO_2018_148_a15
ER  - 
%0 Journal Article
%A V. V. Shurygin (Jr.)
%T On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 130-135
%V 148
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_148_a15/
%G ru
%F INTO_2018_148_a15
V. V. Shurygin (Jr.). On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 130-135. http://geodesic.mathdoc.fr/item/INTO_2018_148_a15/

[1] Bibikov P. V., “Klassifikatsiya upravlyaemykh ansamblei proektivnykh tochek”, Izv. vuzov. Ser. mat., 3 (2015), 28–34 | Zbl

[2] Vinogradov A. M., Krasilschik I. S., Lychagin V. V., Vvedenie v geometriyu nelineinykh differentsialnykh uravnenii, Nauka, M., 1986 | MR

[3] Kushner A. G., Lychagin V. V., “Invarianty Petrova gamiltonovykh sistem s upravlyayuschim parametrom”, Avtomat. telemekh., 3 (2013), 83–102 | Zbl

[4] Olver P., Prilozheniya grupp Li k differentsialnyi uravneniyam, Mir, M., 1989

[5] Appell P., “Sur les invariants de quelques équations différentielles”, J. Math., 5 (1889), 361–423

[6] Gritsenko D. S., Kiriukhin O. M., “Differential invariants of feedback transformations for quasi-harmonic oscillation equations”, J. Geom. Phys., 113 (2017), 65–72 | MR | Zbl

[7] Kruglikov B. S., Lychagin V. V., Global Lie–Tresse theorem, arXiv: 1111.5480 [math.DG] | MR

[8] Lychagin V., “Feedback equivalence of $1$-dimensional control systems of the first order”, Geometry, Topology, and Their Applications, Proc. Inst. Math. NAS Ukraine, v. 6, 2009, 288–302 | Zbl

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