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

Milan Medveď

Annales Polonici Mathematici (1998)

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

Abstract

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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.

How to cite

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Milan 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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  1. [1] R. Abraham and J. Robbin, Transversal Mappings and Flows, W. A. Benjamin, New York, 1967. 
  2. [2] M. Medveď, Oscillatory properties of some classes of nonlinear differential equations, Math. Bohemica 117 (1992), 95-107. 
  3. [3] M. Medveď, Generic bifurcations of second order ordinary diferential equations on differentiable manifolds, Math. Slovaca 27 (1977), 9-24. Zbl0351.58007
  4. [4] M. Medveď, Generic bifurcations of second order ordinary differential equations near closed orbits, J. Differential Equations 36 (1980), 98-107. Zbl0448.58013
  5. [5] M. Medveď, On generic bifurcations of second order ordinary differential equations near closed orbits, Astérisque 50 (1977), 23-29. 
  6. [6] M. Medveď, Fundamentals of Dynamical Systems and Bifurcation Theory, Adam Hilger, Bristol, 1992. Zbl0777.58027
  7. [7] M. Medveď, A class of vector fields on manifolds containing second order ODEs, Hiroshima Math. J. 26 (1996), 127-149. Zbl0852.34043
  8. [8] P. Seibert and R. Suarez, Global stabilization of nonlinear cascade systems, Systems Control Lett. 14 (1990), 347-352. Zbl0699.93073
  9. [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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