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A semiclassical approximation for the matrix elements of a quantum chaoticpropagator in the scar function basis has been derived. The obtained expressionis solely expressed in terms of canonical invariant objects. For our purpose,we have used, the recently developed, semiclassical matrix elements of thepropagator in coherent states, together with the linearization of the flux inthe neighborhood of a classically unstable periodic orbit of chaotic twodimensional systems. The expression here derived is successfully verified to beexact for a (linear) cat map, after the theory is adapted to a discrete phasespace appropriate to a quantized torus.

Semiclassical matrix elements for a chaotic propagator in the Scar functions basis