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For interval maps, given the existence of some specified "types" of periodic orbits, must they also have some other "types" of periodic orbits? This so-called "forcing problem" is interesting, and yet has no easy answer. In this paper, we con- sider three different "types" of periodic orbits and obtain some forcing relations on these periodic orbits. On the other hand, we use the method of symbolic representa- tion to compute the number of periodic points of all periods for the linearizations of these periodic orbits and obtain some interesting new congruence identities in number
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