Relations between chain recurrent points and turning points on the interval
Author:
Shi Hai Li
Journal:
Proc. Amer. Math. Soc. 115 (1992), 265270
MSC:
Primary 58F20; Secondary 26A18, 58F08
MathSciNet review:
1079896
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Abstract: If a point is in the limit set and the limit set of the same point, then we call it a limit point. Then a limit point is an limit point and thus a nonwandering point. In this paper, we prove that, on the interval, a nonwandering point which is not a limit point is in the closure of the set of forward images of turning points, and such points are not always the forward images of turning points. But a nonwandering point which is not an limit point forward image of some turning point. Two examples are given. One shows that a chain recurrent point which is not nonwandering, a limit point which is not recurrent and a recurrent point which is not periodic need not be in the closure of forward images of turning points. The other shows that an limit point which is not a limit point can be a limit point of forward images of turning points but not a forward image nor an limit point of any turning point.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199210798964
PII:
S 00029939(1992)10798964
Keywords:
Chain recurrent point,
nonwandering point,
recurrent point,
turning point,
limit point,
limit point,
limit point
Article copyright:
© Copyright 1992
American Mathematical Society
