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 smoothness of Liouville arcs in Arnol'd tongues
Author(s):
Lionel
Slammert
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1817-1823.
MSC (2000):
Primary 58F03, 58F13, 58F14, 58F11
Posted:
January 23, 2001
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Abstract:
For the generic two parameter family of  circle diffeomorphisms of a general form we prove that the bifurcation arcs which correspond to Liouville irrational rotation numbers are  smooth. As a consequence, we give an explicit formula for the derivative of all non-resonance arcs. Results of Arnol'd, Herman, and others give greater smoothness for a more restricted class of rotation numbers using KAM techniques.
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Additional Information:
Lionel
Slammert
Affiliation:
Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, 7535, South Africa
Address at time of publication:
Faculty of Applied Science, Cape Technikon, Cape Town 2000, South Africa
Email:
lslammert@ctech.ac.za
DOI:
10.1090/S0002-9939-01-06043-9
PII:
S 0002-9939(01)06043-9
Received by editor(s):
August 31, 1999
Posted:
January 23, 2001
Additional Notes:
The author thanks the Department of Mathematics at Boston University for a research fellowship that enabled him to do this research.
Communicated by:
Michael Handel
Copyright of article:
Copyright
2001,
American Mathematical Society
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