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Analytic expanding circle maps with explicit spectra

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Published 20 November 2013 • © 2013 IOP Publishing Ltd & London Mathematical Society
, , Citation Julia Slipantschuk et al 2013 Nonlinearity 26 3231 DOI 10.1088/0951-7715/26/12/3231

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Author e-mails

j.slipantschuk@qmul.ac.uk

o.bandtlow@qmul.ac.uk

w.just@qmul.ac.uk

Author affiliations

1 School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS,UK

Dates

  1. Received 8 April 2013
  2. Published

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0951-7715/26/12/3231

Abstract

We show that for any $\lambda \in \mathbb{C}$ 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 non-negative powers of λ and $\overline{\lambda}$ . As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.

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10.1088/0951-7715/26/12/3231