Shift dynamical systems and remotely almost periodic functions

References

[1] A. G. Baskakov, Investigation of linear differential equations by the methods of the spectral theory of difference operators and linear relations (in Russian), Uspekhi Mat. Nauk 68 (2013), no. 1(409), 77–128; translation in Russian Math. Surveys 68 (2013), 69–116. Search in Google Scholar

[2] A. G. Baskakov, Harmonic and spectral analysis of power bounded operators and bounded semigroups of operators on a Banach space (in Russian), Mat. Zametki 97 (2015), no. 2, 174–190; translation in Math. Notes 97 (2015), 164–178. Search in Google Scholar

[3] A. G. Baskakov, V. E. Strukov and I. I. Strukova, Harmonic analysis of periodic and almost periodic at infinity functions from homogeneous spaces and harmonic distributions, Mat. Sb. 210 (2019), no. 10, 37–90. 10.4213/sm9147Search in Google Scholar

[4] I. U. Bronshteĭn, Extensions of Minimal Transformation Group, Izdat. “Štiinca”, Kishinev, 1975. Search in Google Scholar

[5] D. Cheban, Massera’s theorem for asymptotically periodic scalar differential equations, preprint (2023), https://arxiv.or/abs/2311.03005. Search in Google Scholar

[6] D. Cheban, Remotely almost periodic motions of dynamical systems and solutions of differential equations, XVII International Fast Workshop on Applied and Computational Mathematics, Universidad Nacional de Trujillo, Trujillo (2024), 62–66. Search in Google Scholar

[7] D. Cheban, Two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces, Proceedings of the International Conference MSU (IMCS-60), Vladimir Andrunachievici Institute, Chisinau (2024), 161–166. Search in Google Scholar

[8] D. Cheban, Remotely almost periodic motions of dynamical systems, Bull. Acad. Stiinte Republic Moldova, to appear. Search in Google Scholar

[9] D. N. Cheban, Asymptotically Almost Periodic Solutions of Differential Equations, Hindawi, New York, 2009. 10.1155/9789774540998Search in Google Scholar

[10] D. N. Cheban, Global Attractors of Non-Autonomous Dynamical and Control Systems, 2nd ed., Interdiscip. Math. Sci. 18, World Scientific, Hackensack, 2015. 10.1142/9297Search in Google Scholar

[11] D. N. Cheban, Nonautonomous Dynamics—Nonlinear Oscillations and Global Attractors, Springer Monogr. Math., Springer, Cham, 2020. 10.1007/978-3-030-34292-0Search in Google Scholar

[12] H.-S. Ding, W.-G. Jian, N. V. Minh and G. M. N’Guérékata, Kadets type and Loomis type theorems for asymptotically almost periodic functions, J. Differential Equations 373 (2023), 389–410. 10.1016/j.jde.2023.07.019Search in Google Scholar

[13] K. Gryszka, On asymptotically periodic-like motions in flows, Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018), 45–57. 10.2478/aupcsm-2018-0005Search in Google Scholar

[14] H. R. Henríquez, M. Pierri and P. Táboas, On S-asymptotically ω-periodic functions on Banach spaces and applications, J. Math. Anal. Appl. 343 (2008), no. 2, 1119–1130. 10.1016/j.jmaa.2008.02.023Search in Google Scholar

[15] W.-G. Jian and H.-S. Ding, Tauberian theorems on ℝ + and applications, Proc. Amer. Math. Soc. 152 (2024), no. 11, 4745–4757. 10.1090/proc/16954Search in Google Scholar

[16] S. Kakutani, A proof of Beboutov’s theorem, J. Differential Equations 4 (1968), 194–201. 10.1016/0022-0396(68)90036-3Search in Google Scholar

[17] N. S. Kaluzhina, Slow varying functions at infty, periodic functions at infty and their properties (in Russian), Vestnik VGU (2010), no. 2, 97–102. Search in Google Scholar

[18] M. Kostić and H. C. Koyuncuoğlu, Generalized almost periodic solutions of Volterra difference equations, Malaya J. Mat. 11 (2023), no. S, 149–165. 10.26637/mjm11S/010Search in Google Scholar

[19] M. Kostić and V. Kumar, Remotely c-almost periodic type functions in ℝ n , Arch. Math. (Brno) 58 (2022), no. 2, 85–104. 10.5817/AM2022-2-85Search in Google Scholar

[20] L. H. Loomis, The spectral characterization of a class of almost periodic functions, Ann. of Math. (2) 72 (1960), 362–368. 10.2307/1970139Search in Google Scholar

[21] C. Maulén, S. Castillo, M. Kostić and M. Pinto, Remotely almost periodic solutions of ordinary differential equations, J. Math. 2021 (2021), Article ID 9985454. 10.1155/2021/9985454Search in Google Scholar

[22] A. Pelczar, Asymptotically periodic motions, Bull. Polish Acad. Sci. Math. 33 (1985), no. 5–6, 313–319. Search in Google Scholar

[23] W. M. Ruess and W. H. Summers, Minimal sets of almost periodic motions, Math. Ann. 276 (1986), no. 1, 145–158. 10.1007/BF01450931Search in Google Scholar

[24] D. Sarason, Remotely almost periodic functions, Proceedings of the conference on Banach algebras and several complex variables, Contemp. Math. 32, American Mathematical Society, Providence (1984), 237–242. 10.1090/conm/032/769512Search in Google Scholar

[25] B. A. Ščerbakov and L. V. Koreneva, The preservation of the nature of the recurrence of the solutions of differential equations under perturbations, Differ. Uravn. 10 (1974), 470–475, 572. Search in Google Scholar

[26] G. R. Sell, Topological Dynamics and Ordinary Differential Equations, Van Nostrand Reinhold Math. Stud. 33, Van Nostrand Reinhold, London, 1971. Search in Google Scholar

[27] B. A. Shcherbakov, Recurrent solutions of differential equations and the general theory of dynamical systems (in Russian), Differ. Uravn. 3 (1967), no. 9, 1450–1460; translation in Differ. Equ. 3 (1967), no. 9, 758–763. Search in Google Scholar

[28] B. A. Shcherbakov, Topologic Dynamics and Poisson Stability of Solutions of Differential Equations (in Russian), Izdat. “Štiinca”, Kishinev, 1972. Search in Google Scholar

[29] B. A. Shcherbakov, Poisson Stability of Motions of Dynamical Systems and Solutions of Differential Equations (in Russian), “Shtiintsa”, Kishinev, 1985. Search in Google Scholar

[30] K. S. Sibirskiĭ, Introduction to Topological Dynamics, Redakcionno-Izdat. Otdel Akad. Nauk Moldav. SSR, Kishinev, 1970. Search in Google Scholar

[31] C. Zhang and L. Jiang, Remotely almost periodic solutions to systems of differential equations with piecewise constant argument, Appl. Math. Lett. 21 (2008), no. 8, 761–768. 10.1016/j.aml.2007.08.007Search in Google Scholar

[32] S. Zhang and D. Piao, Time remotely almost periodic viscosity solutions of Hamilton–Jacobi equations, Int. Scholarly Res. Network ISRN 2011 (2011), Article 415358. 10.5402/2011/415358Search in Google Scholar