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Basins of measures on inverse limit spaces for the induced homeomorphism
Published online by Cambridge University Press: 13 October 2009
Abstract
Let f:X→X be continuous and onto, where X is a compact metric space. Let be the inverse limit and F:Y →Y the induced homeomorphism. Suppose that μ is an f-invariant measure, and let m be the measure induced on Y by (μ,μ,…). We show that B is a basin of μ if and only if π−11(B) is a basin of m. From this it follows that if μ is an SRB measure for f on X, then the induced measure m on Y is an inverse-limit SRB measure for F. Conversely, if m is an inverse-limit SRB measure for F on Y, then the induced measure μ on X is an SRB measure for f.
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- Copyright © Cambridge University Press 2009
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