Circle diffeomorphisms forced by expanding circle maps

Analytic Expanding Circle Maps with Explicit Spectra

We show that for any λ ∈ C with |λ| < 1 there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorphic functions) are precisely the nonnegative powers of λ and λ. As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.

Groups of Circle Diffeomorphisms

Circle Diffeomorphisms: Quasi-reducibility and Commuting Diffeomorphisms

In this article, we show two related results on circle diffeomorphisms. The first result is on quasi-reducibility: for a Baire-dense set of α, for any diffeomorphism f of rotation number α, it is possible to accumulate Rα with a sequence hn f h−1 n , hn being a diffeomorphism. The second result is: for a Baire-dense set of α, given two commuting diffeomorphisms f and g, such that f has α for ro...

Rational diffeomorphisms of the circle

We prove an interpolation theorem for rational circle diffeomorphisms: A set of N complex numbers of unit modulus may be mapped to any corresponding set by a ratio of polynomials p(z)/q(z) which restricts an invertible mapping of the unit circle S ⊂ C onto itself.

Growth Sequences for Circle Diffeomorphisms

We obtain results on the growth sequences of the differential for iterations of circle diffeomorphisms without periodic points.