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On the structure of the family of Cherry fields on the torus

Published online by Cambridge University Press:  19 September 2008

Colin Boyd
Colin Boyd
Affiliation:
SES 5.2.2, MLB 5/56, B.T.R.L., Martlesham Heath, Ipswich 1P5 7RE, England
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Abstract

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A class of vector fields on the 2-torus, which includes Cherry fields, is studied. Natural paths through this class are defined and it is shown that the parameters for which the vector field is unstable is the closure of has irrational rotation number}, where ƒ is a certain map of the circle and Rt is rotation through t. This is shown to be a Cantor set of zero Hausdorff dimension. The Cherry fields are shown to form a family of codimension one submanifolds of the set of vector fields. The natural paths are shown to be stable paths.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 27 - 46
Copyright
Copyright © Cambridge University Press 1985

References

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