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On the existence of invariant tori of countable linear systems of differential equations
Teplinsky Yuriy Volodymyrovych 1 , Pasyuk K. V. 2
1 Department of Mathematics, Kamianets-Podilskyi National University named after Ivan Ohienko, Kamianets-Podilskyi, 32302, Ukraine
2 Bukovyna State Financial Academy, Chernivtsi, 58000, Ukraine
Keywords: invariant tori, linear systems of differential equations
Abstract

We find sufficient conditions for the existence of Lipschitz and Hölder invariant tori for linear countable systems of differential-difference equations of general form defined on infinite dimensional tori in the space of bounded numerical sequences.

References

[1] Pasyuk K.V. On the existence of Lipschitz invariant tori of countable linear systems of differential equations containing an infinite number of deviations of the scalar argument // Scientific Bulletin of Chernivtsi University. Mathematics. - Chernivtsi: Ruta, 2008. - Issue 421.— P. 75 - 79.

[2] Samoylenko A.M. On the theory of perturbation of invariant manifolds of dynamic systems // Proc. V Int. Conf. on Nonlinear Oscillations. — T. I: Analytical Methods. — Kyiv: IM ANUSSR, 1970. — P. 495-499.

[3] Samoylenko A.M., Teplinsky Yu.V. Counting systems of differential equations. - Kyiv: Publishing House of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 1993. - 308 p.

[4] Samoilenko A.M., Teplinskiy Yu.V. Countable Systems of Differential Equations. - VSP, Utrecht-Boston, 2003. - 287 p.

[5] Samoilenko A.M., Teplinsky Y.V. Elements of the mathematical theory of evolutionary equations in Banach spaces. — Kyiv: Publishing House of the Institute of Mathematics of the NAS of Ukraine, 2008. - 496 p.

Cite
ACS Style
Teplinsky, Y.V.; Pasyuk , K.V. On the existence of invariant tori of countable linear systems of differential equations. Bukovinian Mathematical Journal. 2018, 1
AMA Style
Teplinsky YV, Pasyuk KV. On the existence of invariant tori of countable linear systems of differential equations. Bukovinian Mathematical Journal. 2018; 1(454).
Chicago/Turabian Style
Yuriy Volodymyrovych Teplinsky, K. V. Pasyuk . 2018. "On the existence of invariant tori of countable linear systems of differential equations". Bukovinian Mathematical Journal. 1 no. 454.
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