The concept of renormalization chaos was developed in ref. [30] where its application to boundary invariant curves and Poincaré recurrences had been discussed. However, this chaos is connected with the random continuous fraction expansion for the rotation number of critical boundary invariant curve. This renormalization chaos is universal since the renormalization dynamics on the critical curve asymptotically is the same for all smooth 2-dimensional canonical maps. In some sense randomness in renormdynamics is external and reproducible (like external fixed random noise). In refs. [47, 56] for the first time it was shown that for a critical invariant torus with two frequencies and fixed rotation numbers (as example the spiral mean had been chosen) the renormalization dynamics is irregular and not universal. Indeed, different similar maps give different renormdynamics for the same fixed rotation numbers. This situation is analogous to a strange attractor for which the number of renormalization step plays the role of time. The above problem of two-frequencies torus is related to the analiticity breaking in two coupled Frenkel-Kontorova chains studied in [61].