Geodesic
Legendre Singularities in Systems of Implicit ODEs and Slow--Fast Dynamical Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 140-153

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Generic properties of regular first integrals of systems of implicit differential equations are considered. In particular, for systems of two equations with two phase variables, a classification of generic bifurcations of integral level surfaces is described. 
@article{TM_2008_261_a10,
     author = {V. M. Zakalyukin and A. O. Remizov},
     title = {Legendre {Singularities} in {Systems} of {Implicit} {ODEs} and {Slow--Fast} {Dynamical} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {140--153},
     publisher = {mathdoc},
     volume = {261},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_261_a10/}
}
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V. M. Zakalyukin; A. O. Remizov. Legendre Singularities in Systems of Implicit ODEs and Slow--Fast Dynamical Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 140-153. http://geodesic.mathdoc.fr/item/TM_2008_261_a10/