On a shadowing lemma in metric spaces

Tibor Žáčik

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 2, page 137-149
  • ISSN: 0862-7959

Abstract

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In the present paper conditions are studied, under which a pseudo-orbit of a continuous map f : M M , where M is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map f .

How to cite

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Žáčik, Tibor. "On a shadowing lemma in metric spaces." Mathematica Bohemica 117.2 (1992): 137-149. <http://eudml.org/doc/29062>.

@article{Žáčik1992,
abstract = {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 $f$.},
author = {Žáčik, Tibor},
journal = {Mathematica Bohemica},
keywords = {shadowing property; shadowing lemma; pseudo-orbit; shadowing property; shadowing lemma; pseudo-orbit},
language = {eng},
number = {2},
pages = {137-149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a shadowing lemma in metric spaces},
url = {http://eudml.org/doc/29062},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Žáčik, Tibor
TI - On a shadowing lemma in metric spaces
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 2
SP - 137
EP - 149
AB - 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 $f$.
LA - eng
KW - shadowing property; shadowing lemma; pseudo-orbit; shadowing property; shadowing lemma; pseudo-orbit
UR - http://eudml.org/doc/29062
ER -

References

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  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). (1989) MR0990862
  4. S. N. Chow K. J. Palmer, The accuгacy of numeгically computed oгbits of dynamical systems, to appear. 
  5. E. M. Coven I. Kan J. A. Yorke, 10.1090/S0002-9947-1988-0946440-2, Trans. Amer. Math. Soc. 308 (1988), 227-247. (1988) MR0946440DOI10.1090/S0002-9947-1988-0946440-2
  6. I. Ekeland, 10.7146/math.scand.a-12005, Math. Scand. 52 (262-268). Zbl0515.58026MR0702957DOI10.7146/math.scand.a-12005
  7. J. E. Franke J. Ғ. Selgrade, Hyperbolicity and chain recurгence, Ј. Diff. Eq. 26(1977), 27-36. (1977) MR0467834
  8. S. M. Hammel J. A. Yorke C. Grebogi, 10.1016/0885-064X(87)90024-0, Ј. Complexity 3 (1987), 136-145. (1987) MR0907194DOI10.1016/0885-064X(87)90024-0
  9. S. M. Hammel J. A. Yorke C. Grebogi, 10.1090/S0273-0979-1988-15701-1, Bull. Ameг. Math. Soc. 19 (1988), 465-470. (1988) MR0938160DOI10.1090/S0273-0979-1988-15701-1
  10. K. R. Meyer G. R. Sell, An analytic proof of the shadowing lemma, Funkcialaj Ekvacioj 30 (1987), 127-133. (1987) MR0915267
  11. K. J. Palmer, 10.1007/978-3-322-96656-8_5, Dynamic Reported 1 (1988), 265-306. (1988) Zbl0676.58025MR0945967DOI10.1007/978-3-322-96656-8_5
  12. C. Robinson, 10.1216/RMJ-1977-7-3-425, Rocky Mount. Ј. Math. 7 (1977), 425-437. (1977) MR0494300DOI10.1216/RMJ-1977-7-3-425

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