Is every approximate trajectory of some process near an exact trajectory of a nearby process? |
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Authors: | Helena E Nusse James A Yorke |
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Institution: | (1) Rijksuniversiteit Groningen, Faculteit der Economische Wetenschappen, Vakgroep Econometrie, Postbus 800, NL-9700 AV Groningen, The Netherlands;(2) Institute for Physical Science and Technology, and Department of Mathematics, University of Maryland, 20742 College Park, MD, USA |
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Abstract: | This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg μ for eitherf μ orF μ withf μ (x)=μx forx≦1/2 andf μ (x)=μ(1?x) forx≧1/2, andF μ (x)=μx(1?x). For a given μ we will say:g μ permits increased parameter shadowing if for each δ x >0 there exists someδ μ >0 and some δ f >0 such that every δ f -pseudog μ -orbit starting in some invariant interval can be δ x -shadowed by a realg α -orbit with α=μ+δ μ . We show thatg μ typically permits increased parameter shadowing. |
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