# The resonance spectrum of the cusp map in the space of analytic functions

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1 Citation (Scopus)

## Abstract

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk \$\{z\in C:|z-q|
Original language English 3746-3758 13 Journal of Mathematical Physics 43 7 https://doi.org/10.1063/1.1483895 Published - 01 Jul 2002

## ASJC Scopus subject areas

• Mathematical Physics
• Physics and Astronomy(all)
• Statistical and Nonlinear Physics