Strange triangular maps of the square
Strange triangular maps of the square
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DOI：
10.1017/s0004972700014222
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发表时间：
1995-06
影响因子：
0.7
通讯作者：
G. Forti;L. Paganoni;J. Smítal
中科院分区：
文献类型：
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作者：
G. Forti;L. Paganoni;J. Smítal
我们证明了正方形I1，F：(x，y)→(f(X)，g(x，y))的连续三角映射在一维情形下表现出不可能的现象。具体地说：(1)具有零拓扑熵的三角映射F可以有一个包含区间{a}×i的极小集，并且可以有非一致回归的回归点；这解决了S.F.Kolyada的两个问题。(2)在满足Per(F)=Fix(F)的映射类中，存在具有正序拓扑熵的非混沌映射和具有零序拓扑熵的混沌映射。
We show that continuous triangular maps of the square I1, F: (x, y) → (f(x), g(x, y)), exhibit phenomena impossible in the one-dimensional case. In particular: (1) A triangular map F with zero topological entropy can have a minimal set containing an interval {a} × I, and can have recurrent points that are not uniformly recurrent; this solves two problems by S.F. Kolyada. (2) In the class of mappings satisfying Per(F) = Fix(F), there are non-chaotic maps with positive sequence topological entropy and chaotic maps with zero sequence topological entropy.