Geodesic
On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a stable cycle
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1003-1013 
S. E. Gorodetski; A. M. Ter-Krikorov. On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a stable cycle. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1003-1013. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a6/
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     author = {S. E. Gorodetski and A. M. Ter-Krikorov},
     title = {On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a~stable cycle},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1003--1013},
     year = {2008},
     volume = {48},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a two-dimensional dynamical system at $-\infty, a process describing the transition from an arbitrary neighborhood of an unstable equilibrium to a stable limit cycle is studied. The system is reduced to the Poincaré normal form. An approximate solution is constructed as a polynomial of degree $2N$ containing only even degrees of the small parameter $\varepsilon$. The functional classes to which the coefficients of this polynomial belong are described. The function space containing the exact solution differing from the approximate one by $O(\varepsilon^{2N+1})$ is determined.

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