Computing invariant measures for expanding circle maps

Michael Keane, Rua Murray, Lai-Sang Young
<span title="1998-01-01">1998</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="" style="color: black;">Nonlinearity</a> </i> &nbsp;
Let f be a sufficiently expanding C 2 circle map. We prove that a certain Markov approximation scheme based on a partition of S 1 into 2 N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2-N; C is a constant depending only on the map f.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1088/0951-7715/11/1/004</a> <a target="_blank" rel="external noopener" href="">fatcat:aiyfi555s5ey5gwyzba5rzn4xq</a> </span>
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