Triangle Map and Its Ergodic Properties Available to Purchase

The triangle map on the torus is a non‐hyperbolic system featuring properties mainly common to chaotic systems such as diffusion, ergodicity and mixing. Here we present some new aspects of ergodicity and mixing in this system. The properties of the triangle map are studied by symbolically encoding the evolution up to some time t using two different schemes: polygonal and binary encoding. The phase space is partitioned in sets of points of same symbolic code. The size of the partitions grows with increasing encoding time as $O(t3).$ The statistical properties of partitions scale with time t, which is closely examined. In addition we calculate the transition probabilities between elements of the partition, referred to as the Markov matrix, and study its spectral gap and Sinai‐Kolmogorov entropy. We find that the gap is shrinking algebraically with increasing time as expected.