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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Communicated by J. N. Mather
Research supported in part by the Netherlands organization for the advancement of pure research (Z.W.O.) and under grant AFOSR-81-0217
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Nusse, H.E., Yorke, J.A. Is every approximate trajectory of some process near an exact trajectory of a nearby process?. Commun.Math. Phys. 114, 363–379 (1988). https://doi.org/10.1007/BF01242136
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DOI: https://doi.org/10.1007/BF01242136