Bifurcation of heteroclinic orbits for diffeomorphisms

Michal Fečkan

Applications of Mathematics (1991)

  • Volume: 36, Issue: 5, page 355-367
  • ISSN: 0862-7940

Abstract

top
The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.

How to cite

top

Fečkan, Michal. "Bifurcation of heteroclinic orbits for diffeomorphisms." Applications of Mathematics 36.5 (1991): 355-367. <http://eudml.org/doc/15684>.

@article{Fečkan1991,
abstract = {The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.},
author = {Fečkan, Michal},
journal = {Applications of Mathematics},
keywords = {bifurcation phenomena; heteroclinic points; discrete dynamical systems; dynamical system; diffeomorphism; bifurcation; dynamical system; heteroclinic orbit; diffeomorphism},
language = {eng},
number = {5},
pages = {355-367},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcation of heteroclinic orbits for diffeomorphisms},
url = {http://eudml.org/doc/15684},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Fečkan, Michal
TI - Bifurcation of heteroclinic orbits for diffeomorphisms
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 5
SP - 355
EP - 367
AB - The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.
LA - eng
KW - bifurcation phenomena; heteroclinic points; discrete dynamical systems; dynamical system; diffeomorphism; bifurcation; dynamical system; heteroclinic orbit; diffeomorphism
UR - http://eudml.org/doc/15684
ER -

References

top
  1. M. Medveď, Dynamical Systems, (Slovak). Veda, Bratislava 1988. (1988) MR0982929
  2. S. Smale, 10.1090/S0002-9904-1967-11798-1, Bull. Amer. Math. Soc. V. 73 (1967), 747- 817. (1967) Zbl0202.55202MR0228014DOI10.1090/S0002-9904-1967-11798-1
  3. V. K. Melnikov, On the stability of the center for the time periodic solutions, Trans. Moscow Math. Soc. V. 12 (1963), 3-56. (1963) MR0156048
  4. K. J. Palmer, 10.1016/0022-0396(84)90082-2, J. Diff. Equations V. 55 (1984), 225-256. (1984) Zbl0508.58035MR0764125DOI10.1016/0022-0396(84)90082-2
  5. M. Golubitsky V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag, New York, Heidelberg, Berlin, 1973, Mir Moskva, 1977. (1973) MR0467801
  6. D. Henry, Geometric Theory of Semilinear Parabolic Equations, LNM 840, Springer-Verlag, New York, Berlin, 1981. (1981) Zbl0456.35001MR0610244
  7. Z. Nitecki, Differentiable Dynamics, The MIT Press, Cambridge, Massachusetts, London, 1971. Mir, Moskva, 1975. (1971) Zbl0246.58012MR0649788
  8. S. N. Chow J. K. Hale J. Mallet-Paret, 10.1016/0022-0396(80)90104-7, J. Differ. Equations V. 37 (1980), 351-373. (1980) MR0589997DOI10.1016/0022-0396(80)90104-7
  9. Th. Bröcker L. Lander, Differentiable Germs and Catastrophes, Cambridge Univ. Press, Cambridge, 1975, Mir. Moskva, 1977. (1975) MR0494220
  10. S. N. Chow J. K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York, Berlin, Heidelberg, 1982. (1982) MR0660633

NotesEmbed ?

top

You must be logged in to post comments.