In the present paper we show that for a topologically mixing map there are considerably many points in the domain whose orbits display highly erratic time dependence, i.e., if f: X->X is a topologically mixing map where X is a compact metric space then for any increasing sequence q sub i of positive integers and any countable subset S dense in X there exists everywhere an uncountable subset C of X satisfying conditions for any s is an element of S. There exists a subsequence p sub i of the sequence q sub i such that lim sub i->infinity/f(sup P)(sub 1)(y)=s for every y is an element of C, and (2) for any n>0, any n distinct points y sub 1, y sub 2,...,y sub n of C and any n points x sub 1,x sub 2,...,x sub n of X there exists a subsequence t sub i of the sequence q sub i such that lim sub i->infinity/ f sup t sub i y sub j =x sub j for every j=1,2,...n. (author). 4 refs. (Atomindex citation 20:038151)
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