Note to the Lagrange stability of excited pendulum type equations
Mathematica Slovaca (1993)
- Volume: 43, Issue: 5, page 617-630
- ISSN: 0232-0525
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topAndres, Ján, and Staněk, Svatoslav. "Note to the Lagrange stability of excited pendulum type equations." Mathematica Slovaca 43.5 (1993): 617-630. <http://eudml.org/doc/34370>.
@article{Andres1993,
author = {Andres, Ján, Staněk, Svatoslav},
journal = {Mathematica Slovaca},
keywords = {higher-order pendulum-type equations; Lagrange stability; problem of Barbashin},
language = {eng},
number = {5},
pages = {617-630},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Note to the Lagrange stability of excited pendulum type equations},
url = {http://eudml.org/doc/34370},
volume = {43},
year = {1993},
}
TY - JOUR
AU - Andres, Ján
AU - Staněk, Svatoslav
TI - Note to the Lagrange stability of excited pendulum type equations
JO - Mathematica Slovaca
PY - 1993
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 43
IS - 5
SP - 617
EP - 630
LA - eng
KW - higher-order pendulum-type equations; Lagrange stability; problem of Barbashin
UR - http://eudml.org/doc/34370
ER -
References
top- 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. (1992) Zbl0763.34038MR1160114
- 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. (1992) Zbl0823.70018
- 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. (1988) MR1062630
- 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. (1989) Zbl0753.34020MR1142529
- BARBASHIN V. A.-TABUEVA E. A., Dynamical Systems with Cylindrical Phase Space, (Russian), Nauka, Moscow, 1964. (1964)
- CHENCINER A., Systèmes dynamiques differentiables, In: Encyclopedia Universalis, Universalia, Paris, 1978. (1978)
- COPPEL W. A., Stability and Asymptotic Behavior of Differential Equations, D.C Heath, Boston, 1965. (1965) Zbl0154.09301MR0190463
- 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. (1982)
- 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. (1988) MR0970558
- GUCKENHEIMER J.-HOLMES P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Appl. Math. Sci. 42, Springer, New York-Berlin, 1984. (1984) MR1139515
- LEONOV G. A., On a problem of Barbashin, Vestnik Leningrad Univ. Math. 13 (1981), 293-297. (1981) MR1279993
- MAWHIN J., Periodic oscillations of forced pendulum-like equations, In: Lecture Notes in Math. 964, Springer, New York-Berlin, 1982. (1982) Zbl0517.34029MR0693131
- MAWHIN J., The forced pendulum: A paradigm for nonlinear analysis and dynamical systems, Exposition. Math. 6 (1988), 271-287. (1988) Zbl0668.70028MR0949785
- MOSER J., Stable and Random Motions in Dynamical Systems, Princeton Univ. Press and Univ. of Tokyo Press, Princeton, 1973. (1973) Zbl0271.70009MR0442980
- ORTEGA R., A counterexample for the damped pendulum equation, Bull. Roy. Acad. Sci. Belgique 73 (1987), 405-409. (1987) Zbl0679.70022MR1026970
- ORTEGA R., Topological degree and stability of periodic solutions for certain differential equations, J. London Math. Soc., (To appear). Zbl0677.34042MR1087224
- PALMER K. J., Exponential dichotomies and transversal homoclinic points, J. Differential Equations 55 (1984), 225-256. (1984) Zbl0508.58035MR0764125
- 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. (1989) MR1009327
- POPOV V. M., Hyperstability of Control Systems, Springer, Berlin, 1973. (1973) Zbl0276.93033MR0387749
- SANDERS J., VERHULST F., Averaging Methods in Nonlinear Dynamical Systems, Appl. Math. Sci. 59, Springer, New York-Berlin, 1985. (1985) Zbl0586.34040MR0810620
- SĘDZIWY S., Boundedness of solutions of an n-th order nonlinear differential equation, Atti Accad. Naz. Lincei 64 (1978), 363-366. (1978) Zbl0421.34040MR0551517
- SEIFERT G., The asymptotic behaviour of solutions of pendulum type equations, Ann. of Math. 69 (1959), 75-87. (1959) MR0100703
- SHAHGIL'DJAN V. V., LJAHOVKIN A. A., Systems of Phase-Shift Automatic Frequency, (Russian), Control. Svjaz, Moscow, 1972. (1972)
- SWICK K. E., Asymptotic behavior of the solutions of certain third order differential equations, SIAM J. Appl. Math. 19 (1970), 96-102. (1970) Zbl0212.11403MR0267212
- TRICOMI F., Integrazione di un'equazione differenziale presentatasi in elettrotecnia, Ann. R. Sc. Norm. Sup. di Pisa 2 (1933), 1-20. (1933) MR1556692
- 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. (1971) Zbl0287.34033MR0320455
- YOU J., Invariant tori and Lagrange stability of pendulum-type equations, J. Differential Equations 85 (1990), 54-65. (1990) Zbl0702.34047MR1052327
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