RUS  ENG
Full version
JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2024 Volume 327, Pages 283–290 (Mi tm4439)
Remarks on Forced Oscillations on Manifolds

I. Yu. Polekhinabcd

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
c Lomonosov Moscow State University, Moscow, Russia
d P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: We find sufficient conditions for the existence of forced oscillations on a manifold in the presence of dissipation in the system. We also give sufficient conditions for the existence of forced oscillations in systems without dissipation in the case when the driving force is small.

Keywords: periodic systems, forced oscillations, friction, dynamics on manifolds.

Received: April 14, 2024
Revised: July 16, 2024
Accepted: September 24, 2024

DOI: 10.4213/tm4439


 English version: Proceedings of the Steklov Institute of Mathematics, 2024, 327, 268–275

Bibliographic databases:

© Steklov Math. Inst. of RAS, 2025