Abstract
The starting point for this paper was the following problem: If we know the invariant densities for two maps S and T can we say something about the invariant density of the map \(U = T \circ S\)? This problem seems not to be touched on within ergodic theory. In this note we look at the inverse problem. Let the invariant density for \(U = T \circ S\) be known. What can we say about invariant densities for S and T? We discuss a simple model, namely the class of all piecewise fractional linear maps with two branches on the unit interval [0, 1].
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Communicated by H. Bruin.
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Schweiger, F. Invariant densities for composed piecewise fractional linear maps. Monatsh Math 194, 181–192 (2021). https://doi.org/10.1007/s00605-020-01475-8
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DOI: https://doi.org/10.1007/s00605-020-01475-8