| Title:
|
On the existence of chaotic behaviour of diffeomorphisms (English) |
| Author:
|
Fečkan, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
101-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt. (English) |
| Keyword:
|
bifurcations |
| Keyword:
|
homoclinic orbits |
| Keyword:
|
chaotic behaviour |
| MSC:
|
34C23 |
| MSC:
|
37G99 |
| MSC:
|
58F08 |
| MSC:
|
58F14 |
| MSC:
|
58F15 |
| MSC:
|
58f30 |
| idZBL:
|
Zbl 0789.58056 |
| idMR:
|
MR1202747 |
| DOI:
|
10.21136/AM.1993.104538 |
| . |
| Date available:
|
2008-05-20T18:45:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104538 |
| . |
| Reference:
|
[1] K. R. Meyer & C. R. Sell: Melnikov transforms, Bernoulli bundles, and almost periodic perturbations.Trans. Amer. Math. Soc. 314 (1) (1989), 63-105. MR 0954601 |
| Reference:
|
[2] K. J. Palmer: Exponential dichotomies, the shadowing lemma and transversal homoclinic points.Dynamics Reported 1 (1988), 265-306. Zbl 0676.58025, MR 0945967, 10.1007/978-3-322-96656-8_5 |
| Reference:
|
[3] K. J. Palmer: Exponential dichotomies and transversal homoclinic points.J. Diff. Equations 55 (1984), 225-256. Zbl 0508.58035, MR 0764125, 10.1016/0022-0396(84)90082-2 |
| Reference:
|
[4] S. N. Chow, J . K. Hale & J. Mallet-Paret: An example of bifurcation to homoclinic orbits.J. Diff. Equations 37 (1980), 351-373. MR 0589997, 10.1016/0022-0396(80)90104-7 |
| Reference:
|
[5] M. Fečkan: Bifurcations of heteroclinic orbits for diffeomorfisms.Aplikace Matematiky 36 (1991), 355-367. MR 1125637 |
| Reference:
|
[6] S. Smale: Diffeomorphisms with infinitely many periodic points.in Differential and Combinatorical Topology, Princeton Univ. Press, New Jersey, 1963, pp. 63-80. MR 0182020 |
| Reference:
|
[7] C. Pugh M. Shub & M. W. Hirsch: Invariant Manifolds.Lec. Not. Math. 583, Springer- -Verlag, New York, 1977. MR 0501173 |
| Reference:
|
[8] S. Wiggins: Global Bifurcations and Chaos.Appl. Math. Sci. 73, Springer- Verlag, New York, 1988. Zbl 0661.58001, MR 0956468, 10.1007/978-1-4612-1042-9 |
| Reference:
|
[9] D. Henry: Geometric Theory of Semilinear Parabolic Equations.Lec. Not. Math. 840, Springer- Verlag, New York, 1981. Zbl 0456.35001, MR 0610244, 10.1007/BFb0089647 |
| Reference:
|
[10] M. W. Hirsh & S. Smale: Differential Equations, Dynamical Systems, and Linear Algebra.Academic Press, New York, 1974. MR 0486784 |
| Reference:
|
[11] M. L. Glasser V. G. Papageoriou & T. C. Bountis: Melnikov's function for two-dimensional mappings.SIAM J. Appl. Math. 49 (1989), 692-703. MR 0997915, 10.1137/0149040 |
| Reference:
|
[12] M. Medveď: Dynamical Systems.Veda, Bratislava, 1988. (In Slovak.) MR 0982929 |
| . |
