| Title:
|
Note to the Lagrange stability of excited pendulum type equations (English) |
| Author:
|
Andres, Ján |
| Author:
|
Staněk, Svatoslav |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
1993 |
| Pages:
|
617-630 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C15 |
| MSC:
|
34D40 |
| MSC:
|
70K20 |
| idZBL:
|
Zbl 0870.34056 |
| idMR:
|
MR1273714 |
| . |
| Date available:
|
2009-09-25T10:52:28Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136594 |
| . |
| Reference:
|
[1] ANDRES J.: Note to the asymptotic behaviour of solutions of damped pendulum equations under forcing.J. Nonlin. Anal. T.M.A. 18 (1992), 705-712. Zbl 0763.34038, MR 1160114 |
| Reference:
|
[2] ANDRES J.: Lagrange stability of higher-order analogy of damped pendulum equations.Acta Univ. Palack. Olomouc. Fac. Rerum Natur. Math. 106, Phys. 31 (1992), 154-159. Zbl 0823.70018 |
| Reference:
|
[3] ANDRES J.: Problem of Barbashin in the case of forcing.In: Qualit. Theory of Differential Equations (Szeged, 1988). Colloq. Math. Soc. János Bolyai 53, North-Holland, Amsterdam-New York, 1989, pp. 9-16. MR 1062630 |
| Reference:
|
[4] ANDRES J.-VLČEK V.: Asymptotic behaviour of solutions to the n-th order nonlinear differential equation under forcing.Rend. 1st. Mat. Univ. Trieste 21 (1989), 128-143. Zbl 0753.34020, MR 1142529 |
| Reference:
|
[5] BARBASHIN V. A.-TABUEVA E. A.: Dynamical Systems with Cylindrical Phase Space.(Russian), Nauka, Moscow, 1964. |
| Reference:
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[6] CHENCINER A.: Systèmes dynamiques differentiables.In: Encyclopedia Universalis, Universalia, Paris, 1978. |
| Reference:
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[7] COPPEL W. A.: Stability and Asymptotic Behavior of Differential Equations.D.C Heath, Boston, 1965. Zbl 0154.09301, MR 0190463 |
| Reference:
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[8] D'HUMIÈRES D.-BEASLEY M. R.-HUBERMAN B. A.-LIBCHABER A.: Chaotic states and routes to chaos in the forced pendulum.Phys. Rev. A 26 (1982), 3483-3496. |
| Reference:
|
[9] GREBOGI, C-NUSSE H. E.-OTT E.-YORKE J. A.: Basic sets: sets that determine the dimension of basin boundaries.In: Lecture Notes in Math. 1342, Springer, New York-Berlin, 1988, pp. 220-250. MR 0970558 |
| Reference:
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[10] GUCKENHEIMER J.-HOLMES P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields.Appl. Math. Sci. 42, Springer, New York-Berlin, 1984. MR 1139515 |
| Reference:
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[11] LEONOV G. A.: On a problem of Barbashin.Vestnik Leningrad Univ. Math. 13 (1981), 293-297. MR 1279993 |
| Reference:
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[12] MAWHIN J.: Periodic oscillations of forced pendulum-like equations.In: Lecture Notes in Math. 964, Springer, New York-Berlin, 1982. Zbl 0517.34029, MR 0693131 |
| Reference:
|
[13] MAWHIN J.: The forced pendulum: A paradigm for nonlinear analysis and dynamical systems.Exposition. Math. 6 (1988), 271-287. Zbl 0668.70028, MR 0949785 |
| Reference:
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[14] MOSER J.: Stable and Random Motions in Dynamical Systems.Princeton Univ. Press and Univ. of Tokyo Press, Princeton, 1973. Zbl 0271.70009, MR 0442980 |
| Reference:
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[15] ORTEGA R.: A counterexample for the damped pendulum equation.Bull. Roy. Acad. Sci. Belgique 73 (1987), 405-409. Zbl 0679.70022, MR 1026970 |
| Reference:
|
[16] ORTEGA R.: Topological degree and stability of periodic solutions for certain differential equations.J. London Math. Soc., (To appear). Zbl 0677.34042, MR 1087224 |
| Reference:
|
[17] PALMER K. J.: Exponential dichotomies and transversal homoclinic points.J. Differential Equations 55 (1984), 225-256. Zbl 0508.58035, MR 0764125 |
| Reference:
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[18] PARK B. S., GREBOGI C., OTT E., YORKE J. A.: Scaling of fractal basin boundaries near intermittency transitions to chaos.Phys. Rev. A 40 (1989), 1576-1581. MR 1009327 |
| Reference:
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[19] POPOV V. M.: Hyperstability of Control Systems.Springer, Berlin, 1973. Zbl 0276.93033, MR 0387749 |
| Reference:
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[20] SANDERS J., VERHULST F.: Averaging Methods in Nonlinear Dynamical Systems.Appl. Math. Sci. 59, Springer, New York-Berlin, 1985. Zbl 0586.34040, MR 0810620 |
| Reference:
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[21] SĘDZIWY S.: Boundedness of solutions of an n-th order nonlinear differential equation.Atti Accad. Naz. Lincei 64 (1978), 363-366. Zbl 0421.34040, MR 0551517 |
| Reference:
|
[22] SEIFERT G.: The asymptotic behaviour of solutions of pendulum type equations.Ann. of Math. 69 (1959), 75-87. MR 0100703 |
| Reference:
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[23] SHAHGIL'DJAN V. V., LJAHOVKIN A. A.: Systems of Phase-Shift Automatic Frequency.(Russian), Control. Svjaz, Moscow, 1972. |
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[24] SWICK K. E.: Asymptotic behavior of the solutions of certain third order differential equations.SIAM J. Appl. Math. 19 (1970), 96-102. Zbl 0212.11403, MR 0267212 |
| Reference:
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[25] TRICOMI F.: Integrazione di un'equazione differenziale presentatasi in elettrotecnia.Ann. R. Sc. Norm. Sup. di Pisa 2 (1933), 1-20. MR 1556692 |
| Reference:
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[26] VORÁČEK J.: On the solution of certain non-linear differential equations of the third order.Acta Univ. Palack. Olomouc. Fac. Rerum Natur. Math. 33 (1971), 147-156. Zbl 0287.34033, MR 0320455 |
| Reference:
|
[27] YOU J.: Invariant tori and Lagrange stability of pendulum-type equations.J. Differential Equations 85 (1990), 54-65. Zbl 0702.34047, MR 1052327 |
| . |
