Geodesic
About the criteria of asymptotic stability of dynamical systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 30-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

The work is devoted to the qualitative theory of stability of dynamical systems on a metric space. A number of stably similar properties of closed invariant sets are presented, on the basis of which equivalent criteria for their asymptotic stability in semi-dynamical systems are formulated.
Keywords: closed invariant set, dynamical system, stability, pseudo-stability, asymptotic stability. 
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B. S. Kalitine. About the criteria of asymptotic stability of dynamical systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 30-38. http://geodesic.mathdoc.fr/item/IVM_2022_9_a2/

[1] Lyapunov A.M., Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhizdat, M.–L., 1950 | MR

[2] Vinograd R.E., “Neprimenimost metoda kharakteristicheskikh pokazatelei k izucheniyu nelineinykh differentsialnykh uravnenii”, Matem. sb. (novaya seriya), 41:4 (1957), 431–438 | Zbl

[3] Antosiewicz H.A., “A survey of Liapunov's second metod”, Contributions to the theory of non-linear oscillation, 1958, no. 4, 141–166 | MR | Zbl

[4] Mendelson B.P., “On unstable attractors”, Boletian Math. Soc. Mexicana, 5:2 (1960), 270–276 | MR | Zbl

[5] Lefschetz S., “Liapunov and stability in dynamical systems”, Boletian Math. Soc. Mexicana, 3:2 (1958), 25–39 | MR | Zbl

[6] Bhatia N.P., “Weak attractors in dynamical systems”, Boletian Math. Soc. Mexicana, 11 (1966), 56–64 | MR

[7] Bhatia N.P., Szegö G., Stability theory of Dynamical systems, Springer, Berlin-Heidelberg-New-York, 1970 | MR | Zbl

[8] Zubov V.I., Ustoichivost dvizheniya. Metody Lyapunova i ikh primenenie, 2-e izd., Vyssh. shk., M., 1984 | MR

[9] Izman M.S., “Ustoichivost i mnozhestva prityazheniya v dispersnykh dinamicheskikh sistemakh”, Matem. issledov., 3, no. 3, RIO AN MSSR, Kishinev, 1968, 60–78 | MR

[10] Kalitin B.S., Kachestvennaya teoriya ustoichivosti dvizheniya dinamicheskikh sistem, BGU, Minsk, 2002

[11] Arredondo J.H., Seibert P., “On a Characterization of Asymptotic Stability”, Aportaciones Matemáticas, Ser. Comunicationes, 29 (2001), 11–16 | MR | Zbl

[12] Kalitine B.S., “About asymptotic stability in semidynamical systems”, Vestn. BGU, Ser. Fiz. Matem. Informatika, 2016, no. 1, 114–119

[13] Hale J.K., Asimptotic Behavior of Dissipative Systems Math, Surv. Monographs. Amer. Math. Soc., 25, 1988 | MR

[14] Ladyzhenskaya O., Attractors for Semigroups and Evolution Equations, Cambridge Univ. Press, 1991 | MR | Zbl

[15] Saperstone S.H., Semidynamical Systems in Infinite Dimentional Space, Springer-Verlag, Berlin, 1981 | MR

[16] Sibirskii K.S., Shube A.S., Poludinamicheskie sistemy, Shtiintsa, Kishinev, 1987 | MR

[17] Birkgof Dzh., Dinamicheskie sistemy, OGIZ–GITL, M.–L., 1941

[18] Kalitin B.S., “Neustoichivost zamknutykh invariantnykh mnozhestv poludinamicheskikh sistem. Metod znakopostoyannykh funktsii Lyapunova”, Matem. zametki, 85:3 (2009), 382–394 | MR | Zbl