Geodesic
Classification of phase portraits of optimal syntheses
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 199-233.

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

The paper is devoted to the investigation of controllable oscillating systems of ordinary differential equations affine in scalar nonsymmetric control in a neighborhood of a singular point of focus or center type. Integrands in value functionals are quadratic in phase coordinates. We classify such systems in case of general position by arising optimal syntheses. The existence of optimal synthesis is proved and its structure is described. 
@article{FPM_2001_7_1_a11,
     author = {R. Hildebrand},
     title = {Classification of phase portraits of optimal syntheses},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {199--233},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a11/}
}
TY  - JOUR
AU  - R. Hildebrand
TI  - Classification of phase portraits of optimal syntheses
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2001
SP  - 199
EP  - 233
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a11/
LA  - ru
ID  - FPM_2001_7_1_a11
ER  - 
%0 Journal Article
%A R. Hildebrand
%T Classification of phase portraits of optimal syntheses
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 199-233
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a11/
%G ru
%F FPM_2001_7_1_a11
R. Hildebrand. Classification of phase portraits of optimal syntheses. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 199-233. http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a11/