Specification on the interval
Specification on the interval
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DOI：
10.1090/s0002-9947-97-01873-4
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发表时间：
1997
影响因子：
1.3
通讯作者：
J. Buzzi
中科院分区：
文献类型：
--
作者：
J. Buzzi
研究了区间映射的不连续性对规范性质的影响。在给出一个分段单调、分段连续的映射具有此性质的充分必要条件后，我们证明了对于一个大的自然类的此类映射（包括，3-变换），其规范性质成立的参数集虽然稠密，但具有零Lebesgue测度.因此，关于规范性质，一般情况与A.M. Blokh（Russian Math. Surveys 38（1983），133-134）解决的连续情况相反（我们对此给出了证明）。
We study the consequences of discontinuities on the specification property for interval maps. After giving a necessary and sufficient condition for a piecewise monotonic, piecewise continuous map to have this property, we show that for a large and natural class of families of such maps (including the ,3-transformations), the set of parameters for which the specification property holds, though dense, has zero Lebesgue measure. Thus, regarding the specification property, the general case is at the opposite of the continuous case solved by A.M. Blokh (Russian Math. Surveys 38 (1983), 133-134) (for which we give a proof).