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arXiv · 1306.0445

Analytic expanding circle maps with explicit spectra

Julia Slipantschuk·Oscar F. Bandtlow·Wolfram Just
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Abstract

We show that for any $λ\in \mathbb{C}$ 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 nonnegative powers of $λ$ and $\barλ$. 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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Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just. 2013-06-03. Analytic expanding circle maps with explicit spectra. https://doi.org/10.1088/0951-7715%2F26%2F12%2F3231

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