CRITICAL CIRCLE MAPS NEAR BIFURCATION

Authors
GRACZYK J SWIATEK G
Citation
J. Graczyk et G. Swiatek, CRITICAL CIRCLE MAPS NEAR BIFURCATION, Communications in Mathematical Physics, 176(2), 1996, pp. 227-260
Citations number
18
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
176
Issue
2
Year of publication
1996
Pages
227 - 260
Database
ISI
SICI code
0010-3616(1996)176:2<227:CCMNB>2.0.ZU;2-5
Abstract
We estimate harmonic scalings in the parameter space of a one-paramete r family of critical circle maps. These estimates lead to the conclusi on that the Hausdorff dimension of the complement of the frequency-loc king set is less than 1 but not less than 1/3. Moreover, the rotation number is a Holder continuous function of the parameter.