# Generic saddle-node bifurcation for cascade second order ODEs on manifolds

Annales Polonici Mathematici (1998)

- Volume: 68, Issue: 3, page 211-225
- ISSN: 0066-2216

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topMilan Medveď. "Generic saddle-node bifurcation for cascade second order ODEs on manifolds." Annales Polonici Mathematici 68.3 (1998): 211-225. <http://eudml.org/doc/270664>.

@article{MilanMedveď1998,

abstract = {Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.},

author = {Milan Medveď},

journal = {Annales Polonici Mathematici},

keywords = {cascade; ODE; critical element; transversal; bifurcation},

language = {eng},

number = {3},

pages = {211-225},

title = {Generic saddle-node bifurcation for cascade second order ODEs on manifolds},

url = {http://eudml.org/doc/270664},

volume = {68},

year = {1998},

}

TY - JOUR

AU - Milan Medveď

TI - Generic saddle-node bifurcation for cascade second order ODEs on manifolds

JO - Annales Polonici Mathematici

PY - 1998

VL - 68

IS - 3

SP - 211

EP - 225

AB - Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

LA - eng

KW - cascade; ODE; critical element; transversal; bifurcation

UR - http://eudml.org/doc/270664

ER -

## References

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- [2] M. Medveď, Oscillatory properties of some classes of nonlinear differential equations, Math. Bohemica 117 (1992), 95-107.
- [3] M. Medveď, Generic bifurcations of second order ordinary diferential equations on differentiable manifolds, Math. Slovaca 27 (1977), 9-24. Zbl0351.58007
- [4] M. Medveď, Generic bifurcations of second order ordinary differential equations near closed orbits, J. Differential Equations 36 (1980), 98-107. Zbl0448.58013
- [5] M. Medveď, On generic bifurcations of second order ordinary differential equations near closed orbits, Astérisque 50 (1977), 23-29.
- [6] M. Medveď, Fundamentals of Dynamical Systems and Bifurcation Theory, Adam Hilger, Bristol, 1992. Zbl0777.58027
- [7] M. Medveď, A class of vector fields on manifolds containing second order ODEs, Hiroshima Math. J. 26 (1996), 127-149. Zbl0852.34043
- [8] P. Seibert and R. Suarez, Global stabilization of nonlinear cascade systems, Systems Control Lett. 14 (1990), 347-352. Zbl0699.93073
- [9] S. Shahshahani, Second order ordinary differential equations on differentiable manifolds, in: Global Analysis, Proc. Sympos. Pure Math. 14, Amer. Math. Soc., 1970, 265-272.

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