The existence problem of a stationary density to a Frobenius-Perron operator will be investigated. Three general existence theorems for Markov operators are presented with the help of the concepts of compactness, quasi-compactness, and constrictiveness. A powerful spectral decomposition theorem for constrictive Markov operators will be given. Then we prove the existence results for three concrete classes of transformations. They are the class of piecewise
and stretching interval mappings, the class of piecewise convex mappings with a weak repellor, and the class of multi-dimensional piecewise
and expanding transformations.
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