Abstract
The structure of the trace formula for quantum maps on a compact phase space is analyzed. An explicit expression for the functional determinant in terms of a finite number of traces is derived which is algebraic and independent of any approximation. For the specific case of the baker's map, its simple structure allows the implementation of a symbolic decomposition of the propagator which is exact and which has the structure of usual semiclassical formulas. The method allows the testing of the accuracy of the individual contribution of each periodic orbit to the functional determinant.
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