Ergodic properties of triangle partitions |
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| Authors: | Ali Messaoudi Arnaldo Nogueira Fritz Schweiger |
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| Institution: | 1.Departamento de Matemática,UNESP-Universidade Estadual Paulista,S?o José do RioPreto,Brazil;2.Institut de Mathématiques de Luminy,Marseille Cedex 9,France;3.Fachbereich Mathematik,Universit?t Salzburg,Salzburg,Austria |
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| Abstract: | 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.
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| Keywords: | Ergodic theory Invariant measures |
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