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Non-existence of invariant circles

Published online by Cambridge University Press:  19 September 2008

John N. Mather
John N. Mather
Affiliation:
Princeton University, Fine Hall, Princeton, NJ 08544, USA
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Abstract

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The dynamical system associated to the difference equation

has been studied numerically by several authors. On the basis of numerical evidence, they conclude that there exists a number k0 ≈ 0.97 such that there are homotopically non-trivial invariant circles for |k|≤k0 and there are none for |k|>k0. In this note, we give a simple rigorous proof that there are none for |k|>.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 301 - 309
Copyright
Copyright © Cambridge University Press 1984

References

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