Geodesic
Singular periodic solutions of polynomial differential equations
Taurida Journal of Computer Science Theory and Mathematics, no. 3 (2024), pp. 74-88 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the problem of periodic solutions of the equation $$\dot z\,=\,z^m+a_1(t)z^{m-1}+\cdots+a_{m-1}(t)z+a_m(t),\quad z\in \mathbb{C},$$ with coefficients $a_k(t),\,k=1,\ldots,m$ periodic in $t$. It is known that equations of this type can have, in addition to ordinary periodic solutions, also special periodic solutions that have a finite number of discontinuities in the period. The compactification procedure for the phase space of an equation makes it possible to determine the conditions that limit the number of ordinary periodic solutions, as well as to describe the mechanism for changing the structure of periodic solutions in terms of rotation numbers.
Keywords: compactification of phase space, periodic solutions, singular periodic solutions, rotation numbers, modromy mapping. 
@article{TVIM_2024_3_a4,
     author = {A. N. Saharov},
     title = {Singular periodic solutions of polynomial differential equations},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
     pages = {74--88},
     year = {2024},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVIM_2024_3_a4/}
}
TY  - JOUR
AU  - A. N. Saharov
TI  - Singular periodic solutions of polynomial differential equations
JO  - Taurida Journal of Computer Science Theory and Mathematics
PY  - 2024
SP  - 74
EP  - 88
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVIM_2024_3_a4/
LA  - ru
ID  - TVIM_2024_3_a4
ER  - 
%0 Journal Article
%A A. N. Saharov
%T Singular periodic solutions of polynomial differential equations
%J Taurida Journal of Computer Science Theory and Mathematics
%D 2024
%P 74-88
%N 3
%U http://geodesic.mathdoc.fr/item/TVIM_2024_3_a4/
%G ru
%F TVIM_2024_3_a4
A. N. Saharov. Singular periodic solutions of polynomial differential equations. Taurida Journal of Computer Science Theory and Mathematics, no. 3 (2024), pp. 74-88. http://geodesic.mathdoc.fr/item/TVIM_2024_3_a4/