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The resonance spectrum of the cusp map in the space of analytic functions. / Antoniou, I.; Shkarin, S. A.; Yarevsky, E.

In: Journal of Mathematical Physics, Vol. 43, No. 7, 01.07.2002, p. 3746-3758.

Research output: Contribution to journal › Article › peer-review

Harvard

Antoniou, I, Shkarin, SA & Yarevsky, E 2002, 'The resonance spectrum of the cusp map in the space of analytic functions', Journal of Mathematical Physics, vol. 43, no. 7, pp. 3746-3758. https://doi.org/10.1063/1.1483895

APA

Antoniou, I., Shkarin, S. A., & Yarevsky, E. (2002). The resonance spectrum of the cusp map in the space of analytic functions. Journal of Mathematical Physics, 43(7), 3746-3758. https://doi.org/10.1063/1.1483895

Vancouver

Antoniou I, Shkarin SA, Yarevsky E. The resonance spectrum of the cusp map in the space of analytic functions. Journal of Mathematical Physics. 2002 Jul 1;43(7):3746-3758. https://doi.org/10.1063/1.1483895

Author

Antoniou, I. ; Shkarin, S. A. ; Yarevsky, E. / The resonance spectrum of the cusp map in the space of analytic functions. In: Journal of Mathematical Physics. 2002 ; Vol. 43, No. 7. pp. 3746-3758.

BibTeX

@article{ddabf23cd561440fb9c4574118d05670,
title = "The resonance spectrum of the cusp map in the space of analytic functions",
abstract = "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 Poincar{\'e} 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.",
author = "I. Antoniou and Shkarin, {S. A.} and E. Yarevsky",
year = "2002",
month = jul,
day = "1",
doi = "10.1063/1.1483895",
language = "English",
volume = "43",
pages = "3746--3758",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "7",

}

RIS

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 -

ID: 36802365