On Asymptotic Contractions
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 218-224.

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A constructive generalization of the contraction mapping principle to the case of mappings with arbitrary rate of contraction is given.
Keywords: attractor, contraction rate, iterative algorithm, dynamical system, intermittency.
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A. A. Kornev; A. M. Stepin. On Asymptotic Contractions. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 218-224. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a5/

[1] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsiii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[2] V. I. Lebedev, Funktsionalnyi analiz i vychislitelnaya matematika, Fizmatlit, M., 2005 | MR | Zbl

[3] A. M. Lyapunov, Obschaya zadacha ob ustoichivosti dvizheniya, Klassiki estestvoznaniya, Gostekhizdat, M., 1950 | MR | Zbl

[4] L. E. Reizin, “Lokalnaya topologicheskaya ekvivalentnost sistem differentsialnykh uravnenii”, Differents. uravneniya, 4 (1968), 199–214 | MR | Zbl

[5] C. Coleman, “Growth and decay estimates near non-elementary stationary points”, Canad. J. Math., 22:6 (1970), 1156–1167 | DOI | MR | Zbl

[6] I. N. Kostin, “Rate of attraction to a non-hyperbolic attractor”, Asymptotic Anal., 1998, no. 16, 203–222 | MR | Zbl

[7] Sh. I. Akhalaya, A. M. Stepin, “Ob invariantnykh merakh neszhimayuschikh otobrazhenii”, Soobsch. AN GSSR, 100:3 (1980), 549–552 | MR | Zbl

[8] Sh. I. Akhalaya, A. M. Stepin, “Ob absolyutno nepreryvnykh invariantnykh merakh neszhimayuschikh preobrazovanii okruzhnosti”, Dinamicheskie sistemy i smezhnye voprosy geometrii, Sbornik statei. Posvyaschaetsya pamyati akademika Andreya Andreevicha Bolibrukha, Tr. MIAN, 244, Nauka, M., 2004, 23–34 | MR | Zbl

[9] A. A. Kornev, “O neustoichivykh mnogoobraziyakh v okrestnosti suschestvenno negiperbolicheskoi tochki”, DAN, 377:6 (2001), 743–745 | MR | Zbl

[10] A. A. Ivanchikov, A. A. Kornev, A. V. Ozeritskii, “O novom podkhode k resheniyu zadach asimptoticheskoi stabilizatsii”, Zh. vychisl. matem. i matem. fiz., 49:12 (2009), 2167–2181 | MR

[11] F. P. Vasilev, Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR | Zbl

[12] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelkov, Chislennye metody, Nauka, M., 1987 | MR | Zbl