Michael Yampolsky 2003 Nonlinearity 16 1565 doi:10.1088/0951-7715/16/5/301
On the eigenvalues of a renormalization operator
Michael Yampolsky
Show affiliationsRecommended by T Prosen
We study the unstable eigenvalues of the renormalization of critical circle maps. The fixed points of this renormalization operator are critical circle maps fn with rotation numbers
ρn = 1/(n+(1/n+...)).We show that the corresponding unstable eigenvalues λn 
n2.
- PACS
- MSC
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37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
15A18 Eigenvalues, singular values, and eigenvectors
37Gxx Local and nonlocal bifurcation theory (See also 34C23, 34K18)
- Subjects
- Dates
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Issue 5 (September 2003)
Received 3 October 2002, in final form 28 May 2003
Published 20 June 2003
A Corrigendum for this article has been published in 2004 Nonlinearity 17 743
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On the eigenvalues of a renormalization operator
Michael Yampolsky 2003 Nonlinearity 16 1565
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