Relations between chain recurrent points and turning points on the interval

Author:
Shi Hai Li

Journal:
Proc. Amer. Math. Soc. **115** (1992), 265-270

MSC:
Primary 58F20; Secondary 26A18, 58F08

DOI:
https://doi.org/10.1090/S0002-9939-1992-1079896-4

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:
https://doi.org/10.1090/S0002-9939-1992-1079896-4

Keywords:
Chain recurrent point,
nonwandering point,
recurrent point,
turning point,
-limit point,
-limit point,
-limit point

Article copyright:
© Copyright 1992
American Mathematical Society