Geodesic
Parametrization of invariant manifolds of slow motions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 33-40

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The method of integral manifolds is used to study the multidimensional systems of differential equations. This approach allows to solve an important problem of order reduction of differential systems. If a slow invariant manifold cannot be described explicitly then its parametrization is used for the system order reduction. In this case, either a part of the fast variables, or all fast variables, supplemented by a certain number of slow variables, can play a role of the parameters.
Mots-clés : singular perturbations, fast variables
Keywords: integral manifold, order reduction, asymptotic expansion, parametrization, differential equations, slow variables. 
@article{VSGU_2018_24_4_a5,
     author = {V. A. Sobolev and E. A. Shchepakina and E. A. Tropkina},
     title = {Parametrization of invariant manifolds of slow motions},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {33--40},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_4_a5/}
}
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V. A. Sobolev; E. A. Shchepakina; E. A. Tropkina. Parametrization of invariant manifolds of slow motions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 33-40. http://geodesic.mathdoc.fr/item/VSGU_2018_24_4_a5/