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Rotation intervals for a class of maps of the real line into itself

Published online by Cambridge University Press:  19 September 2008

Michał Misiurewicz
Michał Misiurewicz
Affiliation:
Institute of Mathematics, Warsaw University, PKiN IX p., 00-901 Warszawa, Poland
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Abstract

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We study a class of maps of the real line into itself which are degree one liftings of maps of the circle and have discontinuities only of a special type. This class contains liftings of continuous degree one maps of the circle, lifting of increasing mod 1 maps and some maps arising from Newton's method of solving equations. We generalize some results known for the continuous case.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 117 - 132
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]Alseda, L., Llibre, J., Misiurewicz, M. & Simo, C.. Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point. Ergod. Th. & Dynam. Sys. 5 (1985), 501–518.CrossRefGoogle Scholar
[2]Bamon, R., Malta, I. P., Pacifico, M. J. & Takens, F.. Rotation intervals of endomorphisms of the circle. Ergod. Th. & Dynam. Sys. 4 (1984), 493–498.CrossRefGoogle Scholar
[3]Hofbauer, F.. Periodic points for piecewise monotonic transformations. Ergod. Th. & Dynam. Sys. 5 (1985), 237–256.CrossRefGoogle Scholar
[4]Ito, R.. Rotation sets are closed. Math. Proc. Camb. Phil. Soc. 89 (1981), 107–111.CrossRefGoogle Scholar
[5]Ito, R.. Note on rotation sets. Proc. Amer. Math. Soc. 89 (1983), 730–732.CrossRefGoogle Scholar
[6]Misiurewicz, M.. Periodic points of maps of degree one of a circle. Ergod. Th. & Dynam. Sys. 2 (1981), 221–227.CrossRefGoogle Scholar
[7]Misiurewicz, M.. Twist sets for maps of a circle. Ergod. Th. & Dynam. Sys. 4 (1984), 391–404.CrossRefGoogle Scholar
[8]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. ubl. Math. IHES 57 (1983), 5–72.CrossRefGoogle Scholar
[9]Saari, D. & Urenko, J.. Newton's method, circle maps, and chaotic motion. Amer. Math. Monthly 91 (1984), 3–17.CrossRefGoogle Scholar