| Title:
|
On a shadowing lemma in metric spaces (English) |
| Author:
|
Žáčik, Tibor |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
137-149 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map $f:M\rightarrow M$, where $M$ is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map $f$. (English) |
| Keyword:
|
shadowing property |
| Keyword:
|
shadowing lemma |
| Keyword:
|
pseudo-orbit |
| MSC:
|
37B99 |
| MSC:
|
37D99 |
| MSC:
|
54C30 |
| MSC:
|
54E35 |
| MSC:
|
54H20 |
| MSC:
|
58F08 |
| MSC:
|
58F15 |
| idZBL:
|
Zbl 0808.54028 |
| idMR:
|
MR1165890 |
| DOI:
|
10.21136/MB.1992.125908 |
| . |
| Date available:
|
2009-09-24T20:51:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125908 |
| . |
| Reference:
|
[1] D. V. Anosov: Geodesic flows on compact Riemannian manifolds of negative curvatuгe.(in Russian), Pгoc. Steklov Inst. Math. 90 (1967), 3-209 English transl., Ameг. Math. Soc. Tгans. (1969). MR 0224110 |
| Reference:
|
[2] R. Bowen: $\omega$-limit sets foг Axiom A diffeomorphisms.J. Diff. Eq. 18 (1975), 333-339. MR 0413181, 10.1016/0022-0396(75)90065-0 |
| Reference:
|
[3] S. N. Chow X. D. Lin K. J. Palmer: A shadowing lemma with applications to semilinear parabolic equations.SIAM J. Math. Anal. 20 (1989). MR 0990862 |
| Reference:
|
[4] S. N. Chow K. J. Palmer: The accuгacy of numeгically computed oгbits of dynamical systems.to appear. |
| Reference:
|
[5] E. M. Coven I. Kan J. A. Yorke: Pseudoorbit shadowing in the family of tent maps.Trans. Amer. Math. Soc. 308 (1988), 227-247. MR 0946440, 10.1090/S0002-9947-1988-0946440-2 |
| Reference:
|
[6] I. Ekeland: Some lemmas about dynamical systems.Math. Scand. 52 (262-268). Zbl 0515.58026, MR 0702957, 10.7146/math.scand.a-12005 |
| Reference:
|
[7] J. E. Franke J. Ғ. Selgrade: Hyperbolicity and chain recurгence.Ј. Diff. Eq. 26(1977), 27-36. MR 0467834 |
| Reference:
|
[8] S. M. Hammel J. A. Yorke C. Grebogi: Do numerical orbits of chaotic dynamical processes гepresent tгue oгbits?.Ј. Complexity 3 (1987), 136-145. MR 0907194, 10.1016/0885-064X(87)90024-0 |
| Reference:
|
[9] S. M. Hammel J. A. Yorke C. Grebogi: Numerical orbits of chaotic pгocesses гepresent tгue orbits.Bull. Ameг. Math. Soc. 19 (1988), 465-470. MR 0938160, 10.1090/S0273-0979-1988-15701-1 |
| Reference:
|
[10] K. R. Meyer G. R. Sell: An analytic proof of the shadowing lemma.Funkcialaj Ekvacioj 30 (1987), 127-133. MR 0915267 |
| Reference:
|
[11] K. J. Palmer: Exponential dichotomies, the shadowing lemma and transversal homoclinic points.Dynamic Reported 1 (1988), 265-306. Zbl 0676.58025, MR 0945967, 10.1007/978-3-322-96656-8_5 |
| Reference:
|
[12] C. Robinson: Stability theorems and hypeгbolicity in dynamical systems.Rocky Mount. Ј. Math. 7 (1977), 425-437. MR 0494300, 10.1216/RMJ-1977-7-3-425 |
| . |
