Abstract: Recognition of various images uses, a presentation of reference (standard) objects transformed into corresponding discretized reference signals without repeating quantization levels. For a set of these signals, a dynamical system is formed of the kind of iterable mapping of d-dimensional cube into itself with limit cycles by the number of reference signals. Representations of an object under identification are transformed into information signals that are applied to the input of the dynamical system as initial conditions and by the results of its functioning a decision is made on recognition of the object under identification. Distinctive features of the method are the conditions of looking through the values of information at the input of the dynamical system and the conditions of determining the correspondence of the information signal to one of the reference signals by the phase trajectory of the dynamical system getting to one of the limit cycles in the process of its functioning.