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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Stratification of continuous maps of an interval


Authors: L. S. Block and W. A. Coppel
Journal: Trans. Amer. Math. Soc. 297 (1986), 587-604
MSC: Primary 58F20; Secondary 26A18, 54C70, 54H20
DOI: https://doi.org/10.1090/S0002-9947-1986-0854086-8
MathSciNet review: 854086
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Abstract: We define the motion of turbulence for a continuous map of an interval into the line and study its relation with periodic and homoclinic points. We define also strongly simple orbits and show, in particular, that they represent periodic orbits with minimum entropy. Further results are obtained for unimodal maps with negative Schwarzian, which sharpen recent results of Block and Hart.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0854086-8
Keywords: Šarkovskii stratification, turbulence, strongly simple orbit, homoclinic point, unimodal map
Article copyright: © Copyright 1986 American Mathematical Society