Abstract
We prove the disjointness ofalmost all interval exchange transformations from ELF systems(systems of probabilistic origin) for a countable subset ofpermutations including the symmetric permutations $ 1\ 2\ \ldots \ m-1 \ m $ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m\ m-1 \ldots \ 2\ 1 $ for m=3,5,7.Some disjointness properties of special flows built over intervalexchange transformations and under piecewise constant rooffunction are investigated as well.
Highlights
ÖÞÝ Ý1⁄2 1⁄2 Å Ø Ñ Ø × ËÙ Ø Ð ×× Ø ÓÒo ¿ 1⁄4 ̧ ¿ 1⁄4 o Ã Ý ÛÓÖ × Ò Ô Ö × ×o ÁÒØ ÖÚ Ð Ü Ò ØÖ Ò× ÓÖÑ Ø ÓÒ× ̧ × Ó ÒØÒ ×× Ó.
×Ù ØØØÖÜ ×Ø × ÕÙ Ò {tn} ⊂ Rtn → +∞ ̧ 0 < α ≤ 1 ̧ J ∈ J (T ) Ò ÔÖÓ Ð ØÝ ÓÖ Ð Ñ ×ÙÖ ÓÒ R ÓÖ Û.
Ttn → α TsdP (s) + (1 − α)J Û ÐÝ Ò L(L2(X, B, μ)).
Summary
1⁄2 1⁄2 Å Ø Ñ Ø × ËÙ Ø Ð ×× Ø ÓÒo ¿ 1⁄4 ̧ ¿ 1⁄4 o Ã Ý ÛÓÖ × Ò Ô Ö × ×o ÁÒØ ÖÚ Ð Ü Ò ØÖ Ò× ÓÖÑ Ø ÓÒ× ̧ × Ó ÒØÒ ×× Ó. ×Ù ØØØÖÜ ×Ø × ÕÙ Ò {tn} ⊂ Rtn → +∞ ̧ 0 < α ≤ 1 ̧ J ∈ J (T ) Ò ÔÖÓ Ð ØÝ ÓÖ Ð Ñ ×ÙÖ ÓÒ R ÓÖ Û. Ttn → α TsdP (s) + (1 − α)J Û ÐÝ Ò L(L2(X, B, μ)). Ô ÖÑÙØ Ø ÓÒ Ó m Ð Ñ ÒØ× ×Ù Ø Ø π(i) + 1 = π(i + 1) ÓÖ 1 ≤ i ≤ m − 1 Ò1⁄2μ π(π−1(1) − 1) = π(1) − 1 ÓÖ π(π−1(m) + 1) = π(m) + 1
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