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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 327, Pages 283–290
DOI: https://doi.org/10.4213/tm4439 (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
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DOI: https://doi.org/10.4213/tm4439
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.
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was supported by the Russian Science Foundation under grant no. 21-71-30011, https://rscf.ru/en/project/21-71-30011/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences.
Received: April 14, 2024
Revised: July 16, 2024
Accepted: September 24, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 327, Pages 268–275
DOI: https://doi.org/10.1134/S0081543824060191
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. Yu. Polekhin, “Remarks on Forced Oscillations on Manifolds”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 283–290; Proc. Steklov Inst. Math., 327 (2024), 268–275
Citation in format AMSBIB
\Bibitem{Pol24}
\by I.~Yu.~Polekhin
\paper Remarks on Forced Oscillations on Manifolds
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 283--290
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4439}
\crossref{https://doi.org/10.4213/tm4439}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 268--275
\crossref{https://doi.org/10.1134/S0081543824060191}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001530768}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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