TY - JOUR

T1 - The resonance spectrum of the cusp map in the space of analytic functions

AU - Antoniou, I.

AU - Shkarin, S. A.

AU - Yarevsky, E.

PY - 2002/7/1

Y1 - 2002/7/1

N2 - We prove that the Frobenius-Perron operator U of the cusp map F:[-1,1] →[-1,1], F(x)= 1 -2 √|x| (which is an approximation of the Poincaré section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any q ∈ (0,1) the spectrum of U in the Hardy space in the disk {z ∈ C:|z - q| < 1 + q} is the union of the segment [0,1] and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.

AB - We prove that the Frobenius-Perron operator U of the cusp map F:[-1,1] →[-1,1], F(x)= 1 -2 √|x| (which is an approximation of the Poincaré section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any q ∈ (0,1) the spectrum of U in the Hardy space in the disk {z ∈ C:|z - q| < 1 + q} is the union of the segment [0,1] and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.

UR - http://www.scopus.com/inward/record.url?scp=0036630008&partnerID=8YFLogxK

U2 - 10.1063/1.1483895

DO - 10.1063/1.1483895

M3 - Article

AN - SCOPUS:0036630008

VL - 43

SP - 3746

EP - 3758

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

ER -