Geodesic
A direct method for calculating Lyapunov values of two-dimensional dynamical systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 119-126

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

A direct method is proposed for studying the behavior of two-dimensional dynamical systems in the critical case when the linear part of the system has two purely imaginary eigenvalues. This method allows one to construct approximations to solutions of the system and to the “turn-round” time of the trajectory in the form of a finite series in powers of the initial datum. With the help of symbolic computations and the proposed method, first approximations of a solution are constructed and expressions for the first three Lyapunov quantities of the Liénard system are written.
Keywords: Lyapunov quantities, limit cycle, symbolic computations. 
@article{TIMM_2010_16_1_a9,
     author = {G. A. Leonov and N. V. Kuznetsov and E. V. Kudryashova},
     title = {A direct method for calculating {Lyapunov} values of two-dimensional dynamical systems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {119--126},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a9/}
}
TY  - JOUR
AU  - G. A. Leonov
AU  - N. V. Kuznetsov
AU  - E. V. Kudryashova
TI  - A direct method for calculating Lyapunov values of two-dimensional dynamical systems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 119
EP  - 126
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a9/
LA  - ru
ID  - TIMM_2010_16_1_a9
ER  - 
%0 Journal Article
%A G. A. Leonov
%A N. V. Kuznetsov
%A E. V. Kudryashova
%T A direct method for calculating Lyapunov values of two-dimensional dynamical systems
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 119-126
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a9/
%G ru
%F TIMM_2010_16_1_a9
G. A. Leonov; N. V. Kuznetsov; E. V. Kudryashova. A direct method for calculating Lyapunov values of two-dimensional dynamical systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 119-126. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a9/