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Keywords:
shadowing property; shadowing lemma; pseudo-orbit
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 $f$.
References:
[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
[2] R. Bowen: $\omega$-limit sets foг Axiom A diffeomorphisms. J. Diff. Eq. 18 (1975), 333-339. DOI 10.1016/0022-0396(75)90065-0 | MR 0413181
[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
[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: Pseudoorbit shadowing in the family of tent maps. Trans. Amer. Math. Soc. 308 (1988), 227-247. DOI 10.1090/S0002-9947-1988-0946440-2 | MR 0946440
[6] I. Ekeland: Some lemmas about dynamical systems. Math. Scand. 52 (262-268). DOI 10.7146/math.scand.a-12005 | MR 0702957 | Zbl 0515.58026
[7] J. E. Franke J. Ғ. Selgrade: Hyperbolicity and chain recurгence. Ј. Diff. Eq. 26(1977), 27-36. MR 0467834
[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. DOI 10.1016/0885-064X(87)90024-0 | MR 0907194
[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. DOI 10.1090/S0273-0979-1988-15701-1 | MR 0938160
[10] K. R. Meyer G. R. Sell: An analytic proof of the shadowing lemma. Funkcialaj Ekvacioj 30 (1987), 127-133. MR 0915267
[11] K. J. Palmer: Exponential dichotomies, the shadowing lemma and transversal homoclinic points. Dynamic Reported 1 (1988), 265-306. DOI 10.1007/978-3-322-96656-8_5 | MR 0945967 | Zbl 0676.58025
[12] C. Robinson: Stability theorems and hypeгbolicity in dynamical systems. Rocky Mount. Ј. Math. 7 (1977), 425-437. DOI 10.1216/RMJ-1977-7-3-425 | MR 0494300
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