Geodesic
On contact equivalence of Abel cubic differential equations of the second order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 93-96.

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We study the geometry of cubic Abel differential equations on one-dimensional real curve. We prove that such an equation is the kernel of some non-linear differential operator. This operator is defined by a cubic on Cartan distribution in $1$-jet space. With the help of this observation we construct contact-invariant $\{e\}$-structure associated with non-degenerated Abel equation and obtain contact classification of such equations.
Keywords: cubic Abel equation, real curve
Mots-clés : jet space, contact pseudogroup, $\{e\}$-structure. 
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     author = {P. V. Bibikov},
     title = {On contact equivalence of {Abel} cubic differential equations of the second order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {93--96},
     publisher = {mathdoc},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_3_a9/}
}
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P. V. Bibikov. On contact equivalence of Abel cubic differential equations of the second order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 93-96. http://geodesic.mathdoc.fr/item/IVM_2016_3_a9/

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