Geodesic
Lyapunov stability of equilibrium states of reversible systems
Matematičeskie zametki, Tome 57 (1995) no. 1, pp. 90-104.

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

@article{MZM_1995_57_1_a7,
     author = {M. V. Matveev},
     title = {Lyapunov stability of equilibrium states of reversible systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {90--104},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_57_1_a7/}
}
TY  - JOUR
AU  - M. V. Matveev
TI  - Lyapunov stability of equilibrium states of reversible systems
JO  - Matematičeskie zametki
PY  - 1995
SP  - 90
EP  - 104
VL  - 57
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_57_1_a7/
LA  - ru
ID  - MZM_1995_57_1_a7
ER  - 
%0 Journal Article
%A M. V. Matveev
%T Lyapunov stability of equilibrium states of reversible systems
%J Matematičeskie zametki
%D 1995
%P 90-104
%V 57
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_57_1_a7/
%G ru
%F MZM_1995_57_1_a7
M. V. Matveev. Lyapunov stability of equilibrium states of reversible systems. Matematičeskie zametki, Tome 57 (1995) no. 1, pp. 90-104. http://geodesic.mathdoc.fr/item/MZM_1995_57_1_a7/

[1] Devaney R. L., “Reversible diffeomorphisms and flows”, Trans. Am. Math. Soc., 218 (1976), 89–113 | DOI | Zbl

[2] Arnol'd V. I., “Reversible systems”, Nonlinear and Turbulent Processes in Physics, 3, ed. R. Z. Sagdeev, Harwood–Chur–N.Y, 1984, 1161–1174

[3] Sevryuk M. B., Reversible systems, Lect. Notes Math., 1211, Springer, Berlin, 1986 | Zbl

[4] Bibikov Yu. N., Local theory of nonlinear analytic ordinary differential equations, Lect. Notes Math., 702, Springer, Berlin, 1979 | Zbl

[5] Roberts J. A. G., Quispel G. R. W., “Chaos and time-reversal symmetry”, Phys. Reports, 216:2–3 (1992), 63–177 | DOI

[6] Sevryuk M. B., “Lower-dimensional tori in reversible systems”, Chaos, 1:2 (1991), 160–167 | DOI | Zbl

[7] Tkhai V. N., “Obratimost mekhanicheskikh sistem”, Prikl. matem. i mekh., 55:4 (1991), 578–586

[8] Montgomery D., Zippin L., Topological transformation groups, Interscience, N.Y., 1955 | Zbl

[9] Kamenkov G. V., Izbrannye trudy, T. 1, Nauka, M., 1971 | Zbl

[10] Bibikov Yu. N., Mnogochastotnye nelineinye kolebaniya i ikh bifurkatsii, LGU, L., 1991

[11] Bryuno A. D., Mnozhestva analitichnosti normalizuyuschego preobrazovaniya, Preprint No 97; Препринт No 98, Ин-т прикл. матем. АН СССР, М., 1974

[12] Bruno A. D., Local methods in nonlinear differential equations, Springer, Berlin, 1989

[13] Douady R., “Stabilité ou instabilité des points fixes elliptiques”, Ann. Scient. Ec. Norm. Sup., 4-e serie, 21 (1988), 1–46 | MR | Zbl

[14] Arnold V. I., “Ob ustoichivosti polozheniya ravnovesiya gamiltonovoi sistemy obyknovennykh differentsialnykh uravnenii v obschem ellipticheskom sluchae”, Dokl. AN SSSR, 137:2 (1961), 255–257 | MR | Zbl

[15] Mozer Yu., Lektsii o gamiltonovykh sistemakh, Mir, M., 1973

[16] Moser J., “Stable and random motions in dynamical systems”, Ann. Math. Stud., 77, Princeton Univ. Press, Princeton, 1973 | Zbl

[17] Moser J., “Convergent series expansions for quasi-periodic motions”, Math. Ann., 169:1 (1967), 136–176 ; Uspekhi mat. nauk, 24:2 (1969), 165–211 | DOI | MR | MR

[18] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1977 | Zbl

[19] Matveev M. V., Ustoichivost obratimykh sistem s dvumya stepenyami svobody, Dep. v VINITI, No 1226-V94, M., 1994

[20] Matveev M. V., Tkhai V. N., “Ustoichivost periodicheskikh obratimykh sistem”, Prikl. matem. i mekh., 57:1 (1993), 3–11 | MR | Zbl