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      Approximation of invariant measures for a class of maps with indifferent fixed points

      Murray, Rua
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      Murray, R.(2005). Approximation of invariant measures for a class of maps with indifferent fixed points. University of Waikato, Mathematics Research Report Series II No. 106. Hamilton, New Zealand: University of Waikato.
      Permanent Research Commons link: https://hdl.handle.net/10289/1745
      Abstract
      Certain dynamical systems on the interval with neutrally stable repelling points admit invariant probability measures which are absolutely continuous with respect to Lebesgue measure. These maps are often used as a model of intermittent dynamics, since they exhibit polynomial rather than exponential decay of correlations (due to the absence of a spectral gap in the underlying transfer operator). This paper presents a class of these maps which are expanding (with convex branches) for which the invariant probability measures can be rigorously approximated by Ulam’s method (a sequence of finite rank approximations to the transfer operator). L1–convergence of the scheme is proved, and some numerical experiments are reported.
      Date
      2005
      Type
      Report
      Series
      Mathematics Research Report Series II
      Report No.
      106
      Publisher
      University of Waikato
      Collections
      • Computing and Mathematical Sciences Papers [1454]
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