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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum chaos and fractals. The transfer operator is sometimes called the Ruelle operator, after David Ruelle, or the Ruelle Perron Frobenius operator in reference to the applicability of the Frobenius Perron theorem to the determination of the eigenvalues of the operator.