Finite orbits in multivalued maps and Bernoulli convolutions
Here two related themes are studied. The first is the existence of network-like orbits arising in multi-valued maps, where orbits naturally have the structure of a branching tree, and a finite orbit has the structure of a tree with branches leading back to lower levels. The second concerns the classical topic of Bernoulli convolutions (these are examples of self-similar measures with overlaps) determined by a numerical parameter. The connection is via a natural map on the interval which is two-valued on the overlap region for the Bernoulli convolution. Here examples of points with specific combinatorial properties are found which are neither Pisot nor Salem numbers.
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