Approximation of invariant measures for a class of maps with indifferent fixed points
Citation
Export citationMurray, 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
2005Type
Report No.
106
Publisher
University of Waikato