I^2连续自映射混沌集合的Hausdorff维数

HAUSDORFF DIMENSION OF CHAOTIC SETS CAUSED BY A CONTINUOUS MAP FROM I^2 INTO ITSELF

把线段连续自映射混沌集合的Hausdorff维数的有关结论推广到I2 上 ,证明了在C°(I2 )中存在一个剩余集R ,使对每一f∈R ,如果集合C I2 对f是Li-Yorke混沌的 ,则C的Hausdorff维数dimH(C) ≤1.

Gu Rongbao discussed Hausdorff dimension of chaotic sets caused by a continuous map into self-mapping of a compact interval I. The result of Gu is extended to I 2, and it is shown that there is a residual set R in C°(I 2) such that for any f∈R , if the set CI 2 is chaotic in the sense of Li-Yorke,then Hausdorff dimension of C is less than or equal to one.