Analytic expanding circle maps with explicit spectra

We show that for any 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 . As a consequence we obtain a counterexample to a variant of a conjecture...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2013-12, Vol.26 (12), p.3231-3245
Main Authors: Slipantschuk, Julia, Bandtlow, Oscar F, Just, Wolfram
Format: Article
Language:English
Subjects:
Eigenvalues
Mathematical analysis
Nonlinearity
Operators
Spectra
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that for any 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 . As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/26/12/3231