| Title:
|
Bifurcation of heteroclinic orbits for diffeomorphisms (English) |
| Author:
|
Fečkan, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
5 |
| Year:
|
1991 |
| Pages:
|
355-367 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
bifurcation phenomena |
| Keyword:
|
heteroclinic points |
| Keyword:
|
discrete dynamical systems |
| Keyword:
|
dynamical system |
| Keyword:
|
diffeomorphism |
| MSC:
|
34C37 |
| MSC:
|
37G99 |
| MSC:
|
58F14 |
| MSC:
|
58f30 |
| idZBL:
|
Zbl 0748.58022 |
| idMR:
|
MR1125637 |
| DOI:
|
10.21136/AM.1991.104472 |
| . |
| Date available:
|
2008-05-20T18:42:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104472 |
| . |
| Reference:
|
[1] M. Medveď: Dynamical Systems.(Slovak). Veda, Bratislava 1988. MR 0982929 |
| Reference:
|
[2] S. Smale: Differentiable dynamical systems.Bull. Amer. Math. Soc. V. 73 (1967), 747- 817. Zbl 0202.55202, MR 0228014, 10.1090/S0002-9904-1967-11798-1 |
| Reference:
|
[3] V. K. Melnikov: On the stability of the center for the time periodic solutions.Trans. Moscow Math. Soc. V. 12 (1963), 3-56. MR 0156048 |
| Reference:
|
[4] K. J. Palmer: Exponential dichotomies and transversal homoclinic points.J. Diff. Equations V. 55 (1984), 225-256. Zbl 0508.58035, MR 0764125, 10.1016/0022-0396(84)90082-2 |
| Reference:
|
[5] M. Golubitsky V. Guillemin: Stable Mappings and their Singularities.Springer-Verlag, New York, Heidelberg, Berlin, 1973, Mir Moskva, 1977. MR 0467801 |
| Reference:
|
[6] D. Henry: Geometric Theory of Semilinear Parabolic Equations.LNM 840, Springer-Verlag, New York, Berlin, 1981. Zbl 0456.35001, MR 0610244 |
| Reference:
|
[7] Z. Nitecki: Differentiable Dynamics.The MIT Press, Cambridge, Massachusetts, London, 1971. Mir, Moskva, 1975. Zbl 0246.58012, MR 0649788 |
| Reference:
|
[8] S. N. Chow J. K. Hale J. Mallet-Paret: An example of bifurcation to homoclinic orbits.J. Differ. Equations V. 37 (1980), 351-373. MR 0589997, 10.1016/0022-0396(80)90104-7 |
| Reference:
|
[9] Th. Bröcker L. Lander: Differentiable Germs and Catastrophes.Cambridge Univ. Press, Cambridge, 1975, Mir. Moskva, 1977. MR 0494220 |
| Reference:
|
[10] S. N. Chow J. K. Hale: Methods of Bifurcation Theory.Springer-Verlag, New York, Berlin, Heidelberg, 1982. MR 0660633 |
| . |
