Analytic expanding circle maps with explicit spectra

Abstract

We show that for any $\lambda \in \mathbb{C}$ with $|\lambda |<1$ 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 $\lambda$ and $\bar{\lambda }$. As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.

15 pages, 3 figures

References in corpus (2)

• On the relation between Lyapunov exponents and exponential decay of correlations
• Explicit a priori bounds on transfer operator eigenvalues

Cited by in corpus (6)

• Complete spectral data for analytic Anosov maps of the torus
• Dynamic mode decomposition for analytic maps
• From dynamical systems with time-varying delay to circle maps and Koopmanism
• Generic non-trivial resonances for Anosov diffeomorphisms
• Transfer operator for ultradifferentiable expanding maps of the circle
• Locating Ruelle-Pollicott resonances