G.-C. Yuan and J. Yorke. An open set of maps for which every point is absolutely nonshadowable. Procs. Amer. Math. Soc., 128:909-918, 2000. Home/Search Document Details and Download
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Dynamical Systems: Moving into the Next Century - Viana (1 citation) (Correct)
....systems [15] asserts that near any pseudo orbit , that is, any sequence (x n ) n such that dist(f(x n ) xn 1 ) is small for all n, there exists a true orbit of the system. Such a strong statement can not be expected to hold in any reasonable generality outside the hyperbolic context, see [11,61]. On the other hand, properties of nite time shadowing for most orbits are implicit in some important situations, e.g. in the proof of stochastic stability of non hyperbolic systems such as the H enon maps [7] Is there a useful shadowing lemma for very general non uniformly hyperbolic systems ....
G.-C. Yuan and J. Yorke. An open set of maps for which every point is absolutely nonshadowable. Procs. Amer. Math. Soc., 128:909-918, 2000.
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