Global pathfollowing of homoclinic orbits in two-parameter ows

@inproceedings{Mathematisches1996GlobalPO,
  title={Global pathfollowing of homoclinic orbits in two-parameter ows},
  author={Bernold Fiedler Mathematisches},
  year={1996}
}
  • Bernold Fiedler Mathematisches
  • Published 1996
The main goal of this paper is a global continuation theorem for homoclinic solutions of autonomous ordinary di erential equations with two real parameters. In one-parameter ows, Hopf bifurcation serves as a starting point for global paths of periodic orbits. B-points, alias Arnol'd-Bogdanov-Takens points, play an analogous role for paths of homoclinic orbits in two-parameter ows. In fact, a path of homoclinic orbits emanating from a B-point can be continued in phase space until it terminates… CONTINUE READING
8 Citations
95 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-8 of 8 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 95 references

Arnol'd (ed.). Dynamical Systems V. Theory of Bifurcations and Catastrophes

  • V I.
  • Enc. Math. Sciences
  • 1992
Highly Influential
10 Excerpts

Homoclinic bifurcations with nonhyperbolic equilibria

  • B. Deng
  • SIAM J. Math. Anal
  • 1990
Highly Influential
4 Excerpts

An index for global Hopf bifurcation in parabolic systems

  • B. Fiedler
  • J. reine angew. Math
  • 1985
Highly Influential
4 Excerpts

Counterexamples to the Seifert conjecture and opening closed leaves of foliations

  • P. A. Schweitzer
  • Ann. of Math
  • 1974
Highly Influential
4 Excerpts

Lectures on bifurcations and versal systems

  • V. I. Arnol'd
  • Russ. Math. Surv
  • 1972
Highly Influential
6 Excerpts

A variational approach to homoclinic orbits in Hamiltonian systems

  • V. Coti Zelati, I. Ekeland, E. S er e
  • Math. Ann
  • 1990
Highly Influential
3 Excerpts

Kirchgassner. A theory of solitary water waves in the presence of surface tension

  • K.C.J. Amick
  • Arch. Rat. Mech. Anal
  • 1989
Highly Influential
4 Excerpts

Whyburn. Topological Analysis

  • G T.
  • 1968
Highly Influential
4 Excerpts

The numerical computation of connecting orbits in dynamical systems

  • W.-J. Beyn
  • IMA Z. Numer. Anal
  • 1990
Highly Influential
3 Excerpts

Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous di erential delay equations. AMS memoir 402

  • H.-O. Walther
  • AMS, Providence,
  • 1989
Highly Influential
2 Excerpts

Similar Papers

Loading similar papers…