Center-Focus Problem for Discontinuous Planar Differential Equations

@article{Gasull2003CenterFocusPF,
  title={Center-Focus Problem for Discontinuous Planar Differential Equations},
  author={Armengol Gasull and Joan Torregrosa},
  journal={I. J. Bifurcation and Chaos},
  year={2003},
  volume={13},
  pages={1755-1765}
}
We study the center-focus problem as well as the number of limit cycles which bifurcate from a weak focus for several families of planar discontinuous ordinary differential equations. Our computations of the return map near the critical point are performed with a new method based on a suitable decomposition of certain one-forms associated with the expression of the system in polar coordinates. This decomposition simplifies all the expressions involved in the procedure. Finally, we apply our… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 20 references

The center problem for discontinuous Liénard differential equation,

  • B. Coll, R. Prohens, A. Gasull
  • Int. J. Bifurcation and Chaos
  • 1999
Highly Influential
6 Excerpts

Non-smooth Dynamical Systems (Springer-Verlag, Berlin)

  • M. Kunze
  • 2000
Highly Influential
4 Excerpts

A relation between small amplitude limit cycles and big limit cycles,

  • A. Gasull, J. Torregrosa
  • Rocky Mountain J. Math
  • 2001
1 Excerpt

Degenerate Hopf bifurcation in discontinuous planar systems,

  • B. Coll, A. Gasull, R. Prohens
  • J. Math. Anal. Appl
  • 2001
2 Excerpts

Center-focus and isochronous center problems for discontinuous differential equations,

  • B. Coll, A. Gasull, R. Prohens
  • Discr. Contin. Dyn. Syst
  • 2000
2 Excerpts

Higher order bifurcations of limit cycles,

  • I. D. Iliev, L. M. Perko
  • J. Diff. Eqs
  • 1999
1 Excerpt

Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem (Birkhäuser Verlag, Basel)

  • R. Roussarie
  • 1998

On second order bifurcations of limit cycles,

  • I. D. Iliev
  • J. London Math. Soc
  • 1998

The successive derivatives of the period function of a plane vector field,

  • J. P. Françoise
  • J. Diff. Eqs
  • 1998

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