Electronic Resource
Springer
Journal of the European Mathematical Society
1 (1999), S. 339-392
ISSN:
1435-9863
Keywords:
Mathematics Subject Classification (1991): 58F03, 58F23
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We prove that two C 3 critical circle maps with the same rotation number in a special set ? are C 1+α conjugate for some α〉0 provided their successive renormalizations converge together at an exponential rate in the C 0 sense. The set ? has full Lebesgue measure and contains all rotation numbers of bounded type. By contrast, we also give examples of C ∞ critical circle maps with the same rotation number that are not C 1+β conjugate for any β〉0. The class of rotation numbers for which such examples exist contains Diophantine numbers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100970050011
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