Ergodic properties of triangle partitions
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We study the ergodic properties of a map called the Triangle Sequence. We prove that the algorithm is weakly convergent almost surely, and ergodic. As far as we know, it is the first example of a 2-dimensional algorithm where a surprising diophantine phenomenon happens: there are sequences of nested cells whose intersection is a segment, although no vertex is fixed. Examples of n-dimensional algorithms presenting this behavior were known for n >= 3.