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We explore the quantum scattering of systems classically described by binaryand other low order Smale horseshoes, in a stage of development where thestable island associated with the inner periodic orbit is large, but chaosaround this island is well developed. For short incoming pulses we findperiodic echoes modulating an exponential decay over many periods. The periodis directly related to the development stage of the horseshoe. We exemplify ourstudies with a one-dimensional system periodically kicked in time and wemention possible experiments.Comment: 7 pages with 6 reduced quality figures! Please contact the authors  (mejia@fis.unam.mx) for an original good quality pre-prin

Quantum and classical echoes in scattering systems described by simple Smale horseshoes