| Title:
|
Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems (English) |
| Author:
|
Meiske, Wolfgang |
| Author:
|
Schneider, Klaus R. |
| Language:
|
English |
| Journal:
|
Časopis pro pěstování matematiky |
| ISSN:
|
0528-2195 |
| Volume:
|
111 |
| Issue:
|
3 |
| Year:
|
1986 |
| Pages:
|
304-313 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C45 |
| idZBL:
|
Zbl 0611.34045 |
| idMR:
|
MR853794 |
| DOI:
|
10.21136/CPM.1986.108154 |
| . |
| Date available:
|
2009-09-23T09:38:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108154 |
| . |
| Reference:
|
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| Reference:
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[2] E. A. Coddington N. Levinson: Theory of ordinary differential equations.McGraw-Hill, New York 1955. MR 0069338 |
| Reference:
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[3] S. Diliberto G. Hufford: Perturbation theorems for nonlinear differential equations.Ann. Math. Stud. 30 (1956), 207-236. MR 0083071 |
| Reference:
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[4] J. K. Hale: Ordinary differential equations.John Wiley & Sons, New York. Zbl 0433.34003, MR 0419901 |
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[5] J. K. Hale: Integral manifolds for perturbed differential systems.Ann. Math. 73 (1961), 496-531. MR 0123786 |
| Reference:
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[6] Ph. Hartman: Ordinary differential equations.Birkhauser, Boston 1982. Zbl 0476.34002, MR 0658490 |
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[7] D. Henry: Geometric theory of semilinear parabolic equations.Lect. Not. Math. 840, Springer, Berlin 1981. Zbl 0456.35001, MR 0610244 |
| Reference:
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[8] G. Iooss: Bifurcation of maps and applications.North-Holland, Amsterdam 1979. Zbl 0408.58019, MR 0531030 |
| Reference:
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[9] T. Kato: Perturbation theory for linear operators.Springer, Berlin 1966. Zbl 0148.12601 |
| Reference:
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[10] A. Kelley: The stable, center-stable, center, center-unstable, unstable manifolds.J. Diff. Eqs. 3(1967), 546-570. Zbl 0173.11001, MR 0221044 |
| Reference:
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[11] H. W. Knobloch F. Kappel: Gewohnliche Differentialgleichungen.Teubner, Stuttgart 1974. MR 0591708 |
| Reference:
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[12] H. W. Knobloch: Hopf bifurcation via integral manifolds.Abh. AdW DDR 1977, 3N, 413-419. Zbl 0363.34031, MR 0508537 |
| Reference:
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[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 0715971 |
| Reference:
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[14] N. M. Krylov N. N. Bogoljubov: Application of methods from nonlinear mechanics to the theory of stationary oscillations.(Russian) Kiev 1934. |
| Reference:
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[15] J. Kurzweil: Exponentially stable integral manifolds, averaging principle and continuous dependence on a parameter.Czech. Mat. J. 16 (1966), 380-423, 463 - 491. Zbl 0186.47701, MR 0206440 |
| Reference:
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[16] J. Kurzweil: Invariant sets of differential systems.(Russian) Diff. Uravn. IV (1968), 785-797. MR 0232044 |
| Reference:
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[17] J. Kurzweil: Invariant manifolds.Comm. Math. Univ. Carol. 11 (1970), 309-336. Zbl 0197.47702, MR 0296963 |
| Reference:
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[18] O. E. Landford: Bifurcation of periodic solutions into invariant tori: the work of Ruelle and Takens.Lect. Not. Math. 322 (1973), 159-192. |
| Reference:
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[19] J. E. Marsden M. McCracken: The Hopf bifurcation and its applictions.Springer, New York 1976. MR 0494309 |
| Reference:
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[20] Ju. A. Mitropoľskij O. B. Lykova: Integral manifolds in the nonlinear mechanics.(Russian) Nauka, Moscow 1973. MR 0364771 |
| Reference:
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[21] V. A. Pliss: Integral manifolds of systems of periodic differential equations.(Russian) Nauka, Moscow 1977. |
| Reference:
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[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 0168851 |
| Reference:
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[23] L. E. Reizinš: Local equivalence of differential equations.(Russian) Zinatne, Riga 1971. |
| Reference:
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[24] K. R. Schneider: Hopf bifurcation and center manifolds.Coll. Math. Soc J. Bolyai 30 (1979), 953-970. MR 0680628 |
| Reference:
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[25] K. R. Schneider: On the application of integral manifolds to Hopf bifurcation.Math. Nachr. 97 (1980), 313-323. Zbl 0478.34038, MR 0600844 |
| Reference:
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[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 0447.58026 |
| Reference:
|
[27] A. H. Wallace: Differential Topology.Benjamin. New York 1968. Zbl 0164.23805 |
| . |
