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An investigation of dynamical properties of solutions of toy model ofinteracting Pomerons with triple vertex in zero transverse dimension isperformed. Stable points and corresponding solutions at the limit of largerapidity are studied in the framework of given model. A presence of closedcycles in solutions is discussed as well as an application of obtained resultsfor the case of interacting QCD Pomerons.

On asymptotic solutions of RFT in zero transverse dimensions