Abstract
We consider compact Lie group extensions of expanding maps of the circle, essentially restricting to SU(2) extensions. The main objective of the paper is the associated Ruelle transfer (or pull-back) operator . Harmonic analysis yields a natural decomposition , where j indexes irreducible representation spaces. Using semi-classical techniques we extend a previous result by Faure proving an asymptotic spectral gap for the family when restricted to adapted spaces of distributions. Our main result is a fractal Weyl upper bound for the number of eigenvalues (the Ruelle resonances) of these operators out of some fixed disc centred on 0 in the complex plane.
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