@article{10_21136_CPM_1986_108154,
author = {Meiske, Wolfgang and Schneider, Klaus R.},
title = {Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems},
journal = {\v{C}asopis pro p\v{e}stov\'an{\'\i} matematiky},
pages = {304--313},
year = {1986},
volume = {111},
number = {3},
doi = {10.21136/CPM.1986.108154},
mrnumber = {853794},
zbl = {0611.34045},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.108154/}
}
TY - JOUR AU - Meiske, Wolfgang AU - Schneider, Klaus R. TI - Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems JO - Časopis pro pěstování matematiky PY - 1986 SP - 304 EP - 313 VL - 111 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.108154/ DO - 10.21136/CPM.1986.108154 LA - en ID - 10_21136_CPM_1986_108154 ER -
%0 Journal Article %A Meiske, Wolfgang %A Schneider, Klaus R. %T Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems %J Časopis pro pěstování matematiky %D 1986 %P 304-313 %V 111 %N 3 %U http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.108154/ %R 10.21136/CPM.1986.108154 %G en %F 10_21136_CPM_1986_108154
Meiske, Wolfgang; Schneider, Klaus R. Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems. Časopis pro pěstování matematiky, Tome 111 (1986) no. 3, pp. 304-313. doi: 10.21136/CPM.1986.108154
[1] N. N. Bogoljubov, Ju. A. Mitropoľskij: Asymptotic methods in the theory of nonlinear oscillations. (Russian) Moscow 1955.
[2] E. A. Coddington N. Levinson: Theory of ordinary differential equations. McGraw-Hill, New York 1955. | MR
[3] S. Diliberto G. Hufford: Perturbation theorems for nonlinear differential equations. Ann. Math. Stud. 30 (1956), 207-236. | MR
[4] J. K. Hale: Ordinary differential equations. John Wiley & Sons, New York. | MR | Zbl
[5] J. K. Hale: Integral manifolds for perturbed differential systems. Ann. Math. 73 (1961), 496-531. | MR
[6] Ph. Hartman: Ordinary differential equations. Birkhauser, Boston 1982. | MR | Zbl
[7] D. Henry: Geometric theory of semilinear parabolic equations. Lect. Not. Math. 840, Springer, Berlin 1981. | MR | Zbl
[8] G. Iooss: Bifurcation of maps and applications. North-Holland, Amsterdam 1979. | MR | Zbl
[9] T. Kato: Perturbation theory for linear operators. Springer, Berlin 1966. | Zbl
[10] A. Kelley: The stable, center-stable, center, center-unstable, unstable manifolds. J. Diff. Eqs. 3(1967), 546-570. | MR | Zbl
[11] H. W. Knobloch F. Kappel: Gewohnliche Differentialgleichungen. Teubner, Stuttgart 1974. | MR
[12] H. W. Knobloch: Hopf bifurcation via integral manifolds. Abh. AdW DDR 1977, 3N, 413-419. | MR | Zbl
[13] H. W. Knobloch B. Aulbach: The role of center manifolds in ordinary differential equations. Teubner-Texte zur Mathematik 47, 179-189. Leipzig 1982. | MR
[14] N. M. Krylov N. N. Bogoljubov: Application of methods from nonlinear mechanics to the theory of stationary oscillations. (Russian) Kiev 1934.
[15] J. Kurzweil: Exponentially stable integral manifolds, averaging principle and continuous dependence on a parameter. Czech. Mat. J. 16 (1966), 380-423, 463 - 491. | MR | Zbl
[16] J. Kurzweil: Invariant sets of differential systems. (Russian) Diff. Uravn. IV (1968), 785-797. | MR
[17] J. Kurzweil: Invariant manifolds. Comm. Math. Univ. Carol. 11 (1970), 309-336. | MR | Zbl
[18] O. E. Landford: Bifurcation of periodic solutions into invariant tori: the work of Ruelle and Takens. Lect. Not. Math. 322 (1973), 159-192.
[19] J. E. Marsden M. McCracken: The Hopf bifurcation and its applictions. Springer, New York 1976. | MR
[20] Ju. A. Mitropoľskij O. B. Lykova: Integral manifolds in the nonlinear mechanics. (Russian) Nauka, Moscow 1973. | MR
[21] V. A. Pliss: Integral manifolds of systems of periodic differential equations. (Russian) Nauka, Moscow 1977.
[22] L. E. Reizinš: Systems of differential equations in local coordinates in the neighbourhood of a closed trajectory. (Russian) Izv. AN Latv. SSR, ser. fiz. techn. nauk 1, (1964), 59-66. | MR
[23] L. E. Reizinš: Local equivalence of differential equations. (Russian) Zinatne, Riga 1971.
[24] K. R. Schneider: Hopf bifurcation and center manifolds. Coll. Math. Soc J. Bolyai 30 (1979), 953-970. | MR
[25] K. R. Schneider: On the application of integral manifolds to Hopf bifurcation. Math. Nachr. 97 (1980), 313-323. | MR | Zbl
[26] K. R. Schneider: On the existence of perturbed center submanifolds of a class of autonomous differential systems. Preprint P-26/80 ZIMM der AdW der DDR. | Zbl
[27] A. H. Wallace: Differential Topology. Benjamin. New York 1968. | Zbl
Cité par Sources :