Bifurcation of heteroclinic orbits for diffeomorphisms
Fečkan, Michal
Applications of Mathematics, Tome 36 (1991), p. 355-367 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1991-01-01
Classification:  34C37,  37G99,  58F14,  58f30
@article{104472,
     author = {Michal Fe\v ckan},
     title = {Bifurcation of heteroclinic orbits for diffeomorphisms},
     journal = {Applications of Mathematics},
     volume = {36},
     year = {1991},
     pages = {355-367},
     zbl = {0748.58022},
     mrnumber = {1125637},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104472}
}
Fečkan, Michal. Bifurcation of heteroclinic orbits for diffeomorphisms. Applications of Mathematics, Tome 36 (1991) pp. 355-367. http://gdmltest.u-ga.fr/item/104472/

M. Medveď Dynamical Systems, (Slovak). Veda, Bratislava 1988. (1988) | MR 0982929

S. Smale Differentiable dynamical systems, Bull. Amer. Math. Soc. V. 73 (1967), 747- 817. (1967) | Article | MR 0228014 | Zbl 0202.55202

V. K. Melnikov On the stability of the center for the time periodic solutions, Trans. Moscow Math. Soc. V. 12 (1963), 3-56. (1963) | MR 0156048

K. J. Palmer Exponential dichotomies and transversal homoclinic points, J. Diff. Equations V. 55 (1984), 225-256. (1984) | Article | MR 0764125 | Zbl 0508.58035

M. Golubitsky V. Guillemin Stable Mappings and their Singularities, Springer-Verlag, New York, Heidelberg, Berlin, 1973, Mir Moskva, 1977. (1973) | MR 0467801

D. Henry Geometric Theory of Semilinear Parabolic Equations, LNM 840, Springer-Verlag, New York, Berlin, 1981. (1981) | MR 0610244 | Zbl 0456.35001

Z. Nitecki Differentiable Dynamics, The MIT Press, Cambridge, Massachusetts, London, 1971. Mir, Moskva, 1975. (1971) | MR 0649788 | Zbl 0246.58012

S. N. Chow J. K. Hale J. Mallet-Paret An example of bifurcation to homoclinic orbits, J. Differ. Equations V. 37 (1980), 351-373. (1980) | Article | MR 0589997

Th. Bröcker L. Lander Differentiable Germs and Catastrophes, Cambridge Univ. Press, Cambridge, 1975, Mir. Moskva, 1977. (1975) | MR 0494220

S. N. Chow J. K. Hale Methods of Bifurcation Theory, Springer-Verlag, New York, Berlin, Heidelberg, 1982. (1982) | MR 0660633