Minimum and maximum value of the classical Peres invariant

Figure 1: freg (B, E=0)
Calculated using the sections of regularity. Grey lines indicate the global minimum of the regularity at B≈0.24 and a local minimum at B≈0.53.
Figure 2: Minimum and maximum value of the classical Peres invariant L^2.
In the vicinity of B=0.24, the system is almost ergodic. In addition, the value of the time averaged value of the Peres invariant inside the remaining regular island is very close to that of the chaotic region. This creates the structure of a "neck". The fluctuation of the minimum value of the Peres invariant on the interval 0.45≤B≤0.6 is caused by rapid appearance and disappearance of various regular islands.