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Rotation intervals of endomorphisms of the circle

Published online by Cambridge University Press:  19 September 2008

R. Bamon ,
I. P. Malta ,
M. J. Pacifico  and
F. Takens
R. Bamon
Affiliation:
Departamento de Matemáica, Universidad de Chile, Casilla 653—Santiago, Chile;
I. P. Malta
Affiliation:
Departamento de Matemdáca, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente, 225, Casa B, CEP 22.453—Gávea—Rio de Janeiro RJ—; Brazil;
M. J. Pacifico
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP 21.910—Rio de Janeiro RJ—Brazil;
F. Takens
Affiliation:
Mathematisch Instituut, Postbus 800, 9700 AV Groningen, The Netherlands
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Abstract

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The rotation number of a diffeomorphism f: S1 → S1 with lift is defined as . We investigate the case where f is an endomorphism. Then this limit may not exist and may depend on x. We investigate the set of limit points of , as a function of x.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 493 - 498
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

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[2]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. IHES Publ. Math. 57 (1983), 5–71.CrossRefGoogle Scholar