Geodesic
Buffer phenomenon in systems close to two-dimensional Hamiltonian ones
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 109-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Plane Hamiltonian systems perturbed by small time-periodic terms are considered. The conditions are established under which exponentially stable periodic solutions are accumulated infinitely in these systems as the perturbations tend to zero or, in other words, the buffer phenomenon occurs. It is shown that this phenomenon is typical for a wide range of classical mechanical problems described by equations of the pendulum type. 
@article{TIMM_2006_12_1_a9,
     author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
     title = {Buffer phenomenon in systems close to two-dimensional {Hamiltonian} ones},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {109--141},
     year = {2006},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a9/}
}
TY  - JOUR
AU  - A. Yu. Kolesov
AU  - E. F. Mishchenko
AU  - N. Kh. Rozov
TI  - Buffer phenomenon in systems close to two-dimensional Hamiltonian ones
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2006
SP  - 109
EP  - 141
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a9/
LA  - ru
ID  - TIMM_2006_12_1_a9
ER  - 
%0 Journal Article
%A A. Yu. Kolesov
%A E. F. Mishchenko
%A N. Kh. Rozov
%T Buffer phenomenon in systems close to two-dimensional Hamiltonian ones
%J Trudy Instituta matematiki i mehaniki
%D 2006
%P 109-141
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a9/
%G ru
%F TIMM_2006_12_1_a9
A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Buffer phenomenon in systems close to two-dimensional Hamiltonian ones. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 109-141. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a9/

[1] Vitt A. A., “Raspredelennye avtokolebatelnye sistemy”, Zhurn. tekhnich. fiziki, 4:1 (1934), 144–157

[2] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Asimptoticheskie metody issledovaniya periodicheskikh reshenii nelineinykh giperbolicheskikh uravnenii”, Tr. MIAN, 222, Nauka, M., 1998, 7–191

[3] Kolesov A. Yu., Rozov N. Kh., Sushko V. G., “Spetsifika avtokolebatelnykh protsessov v rezonansnykh giperbolicheskikh sistemakh”, Fund. i prikl. matematika, 5:2 (1999), 437–473 | MR | Zbl

[4] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Yavlenie bufernosti v rezonansnykh sistemakh giperbolicheskikh uravnenii”, UMN, 55:2(332) (2000), 95–120 | MR | Zbl

[5] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v RCLG-avtogeneratore: teoreticheskii analiz i rezultaty eksperimenta”, Tr. MIAN, 233, 2001, 153–207 | MR | Zbl

[6] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v raspredelennykh mekhanicheskikh sistemakh”, Prikl. matematika i mekhanika, 65:2 (2001), 183–198 | MR | Zbl

[7] Mischenko E. F., Sadovnichii V. A., Kolesov A. Yu., Rozov N. Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei, Fizmatlit, M., 2005

[8] Turing A., “The chemical basis of morphogenesis”, Phil. Trans. Roy. Soc. Lond., 237 (1952), 37–72 | DOI

[9] Zaslavskii G. M., Sagdeev R. Z., Vvedenie v nelineinuyu fiziku. Ot mayatnika do turbulentnosti i khaosa, Nauka, M., 1988 | MR

[10] Zaslavskii G. M., Fizika khaosa v gamiltonovykh sistemakh, In-t kompyuternykh issledovanii, Moskva–Izhevsk, 2004

[11] Melnikov V. K., “Ustoichivost tsentra pri periodicheskikh po vremeni vozmuscheniyakh”, Tr. MMO, 12, 1963, 3–52

[12] Morozov A. D., Shilnikov L. P., “O nekonservativnykh periodicheskikh sistemakh, blizkikh k dvumernym gamiltonovym”, Prikl. matematika i mekhanika, 47:3 (1983), 385–394 | MR

[13] Morozov A. D., Globalnyi analiz v teorii nelineinykh kolebanii, Izd-vo Nizhegorodskogo universiteta, Nizhnii Novgorod, 1995 | Zbl

[14] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, In-t kompyuternykh issledovanii, Moskva–Izhevsk, 2002

[15] Puankare A., Izbrannye trudy v trekh tomakh. Tom I. Novye metody nebesnoi mekhaniki, Nauka, M., 1971 | MR

[16] Kozlov V. V., Simmetrii, topologiya i rezonansy v gamiltonovoi mekhanike, Izd-vo Udmurtskogo gos. universiteta, Izhevsk, 1995 | MR | Zbl

[17] Bryuno A. D., Lokalnyi metod nelineinogo analiza differentsialnykh uravnenii, Nauka, M., 1979 | MR

[18] Katok A. B., Khasselblat B., Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem, Faktorial, M., 1999

[19] Kuznetsov S. P., Dinamicheskii khaos (kurs lektsii), Fizmatlit, M., 2001

[20] Kozlov V. V., “Rasscheplenie separatris i rozhdenie izolirovannykh periodicheskikh reshenii v gamiltonovykh sistemakh s polutora stepenyami svobody”, UMN, 41:5 (1986), 177–178 | MR | Zbl

[21] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. T. 1. Mekhanika, Nauka, M., 1988 | MR

[22] Uitteker E. T., Vatson Dzh N., Kurs sovremennogo analiza. Ch. 2. Transtsendentnye funktsii, Fizmatlit, M., 1963

[23] Abramovitz M., Stegun I., Handbook of mathematical functions, National Bureau of Standard, U.S.A, 1964

[24] Arnold V. I., Avets A., Ergodicheskie problemy klassicheskoi mekhaniki, Izhevskaya respublikanskaya tipografiya, Izhevsk, 1999 | Zbl

[25] Mozer Yu., KAM-teoriya i problemy ustoichivosti, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001 | Zbl

[26] http://tracer3.narod.ru

[27] Gavrilov N. K., Shilnikov L. P., “O trekhmernykh dinamicheskikh sistemakh, blizkikh k sisteme s negruboi gomoklinicheskoi krivoi. I”, Matem. sb., 88:4 (1972), 475–492 | MR | Zbl

[28] Gavrilov N. K., Shilnikov L. P., “O trekhmernykh dinamicheskikh sistemakh, blizkikh k sisteme s negruboi gomoklinicheskoi krivoi. II”, Matem. sb., 90(132):1 (1973), 139–156 | MR | Zbl