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A note on periodic points of expanding maps of the interval

Published online by Cambridge University Press:  17 April 2009

Bau-Sen Du
Bau-Sen Du
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, Republic of China
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Abstract

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We sharpen a result of Byers on the existence of periodic points for some continuous expanding maps of the interval and generalize it to some classes of continuous maps of the interval which are not necessarily expanding. We then use these results to construct one-parameter families of continuous maps of the interval which have a bifurcation form fixed points directly to period 3 points together with a series of reverse bifurcations from period 3 points back to fixed points. Consequently, our results also provide examples of one-parameter families of continuous maps of the interval whose topological entropy jumps form zero to some positive number and then changes back to zero as the parameter varies.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 435 - 447
Copyright
Copyright © Australian Mathematical Society 1986

References

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