Geodesic
Generic phase transitions and profit singularities in Arnol'd's model
Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 17-37

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

For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families. Bibliography: 16 titles. 
@article{SM_2007_198_1_a1,
     author = {A. A. Davydov and H. Mena Matos},
     title = {Generic phase transitions and profit singularities in {Arnol'd's} model},
     journal = {Sbornik. Mathematics},
     pages = {17--37},
     publisher = {mathdoc},
     volume = {198},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_1_a1/}
}
TY  - JOUR
AU  - A. A. Davydov
AU  - H. Mena Matos
TI  - Generic phase transitions and profit singularities in Arnol'd's model
JO  - Sbornik. Mathematics
PY  - 2007
SP  - 17
EP  - 37
VL  - 198
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2007_198_1_a1/
LA  - en
ID  - SM_2007_198_1_a1
ER  - 
%0 Journal Article
%A A. A. Davydov
%A H. Mena Matos
%T Generic phase transitions and profit singularities in Arnol'd's model
%J Sbornik. Mathematics
%D 2007
%P 17-37
%V 198
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2007_198_1_a1/
%G en
%F SM_2007_198_1_a1
A. A. Davydov; H. Mena Matos. Generic phase transitions and profit singularities in Arnol'd's model. Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 17-37. http://geodesic.mathdoc.fr/item/SM_2007_198_1_a1/