منابع مشابه
Density of the Periodic Points in the Interval Set
The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.
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We show that for a continuous map of a closed interval to itself, if the set of periodic points is closed, then every recurrent point is periodic. If, furthermore, the set of least periods of the periodic points is finite, then every nonwandering point is periodic. This answers a question of L. Block [Proc. Amer. Math. Soc. 67 (1977), 357-360]. Introduction. In [1] and [2], L. Block studied con...
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We consider the rotation set ρ(F ) for a lift F of an area preserving homeomorphism f : T → T, which is homotopic to the identity. The relationship between this set and the existence of periodic points for f is least well understood in the case when this set is a line segment. We show that in this case if a vector v lies in ρ(F ) and has both co-ordinates rational, then there is a periodic poin...
متن کاملPeriodic Points
B-spaces are a class of uniquely arcwise connected generalized continua, containing trees. In this paper, it is shown that a main result obtained by several authors for existence of periodic points of small periods of mappings of trees is also true for B-spaces.
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The set of periodic points of self-maps of intervals has been studied for different reasons. The functions with smaller sets of periodic points are more likely not to share a periodic point. Of course, one has to decide what “big” or “small” means and how to describe this notion. In this direction one would be interested in studying the size of the sets of periodic points of self-maps of an int...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2013
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2013.47133