Geodesic
A Practical Two-Dimensional Ergodic Theorem
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 352-357

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Let τ:[0, 1] → [0, 1] be defined by τ(x) = 2x on [0, 1/2,] and τ(JC) = 2(1 - x) on [5, 1], and let T:[0, 1] x [0, 1] → [0, 1] x [0, 1] be defined by T(x,y) = (τ(x), τ(y))- Let where p is a prime > 2, and a and M are integers. Consider T restricted to θM x θN, 1 < M < N. Let X = ((2a)/(pM), (2b)/(pN)) ∈ θM x θN and let per(X) denote the length of the period of X.Then, where m is Lebesque measure on [0, 1], and C is independent of p, N, M, a and b. Thus, as p → or as N - M and M→ →,
DOI : 10.4153/CMB-1986-054-x
Mots-clés : 28D10, 26A1 
Scarowsky, Manny; Boyarsky, Abraham. A Practical Two-Dimensional Ergodic Theorem. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 352-357. doi: 10.4153/CMB-1986-054-x
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     title = {A {Practical} {Two-Dimensional} {Ergodic} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {352--357},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-054-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-054-x/}
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