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Golden mean renormalization for a generalized Harper equation: The strong coupling fixed point

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posted on 03.02.2006, 12:25 by B.D. Mestel, Andrew H. Osbaldestin
We construct a renormalisation fixed point corresponding to the strong coupling limit of the golden mean Harper equation. We give an analytic expression for this fixed point, establish its existence and uniqueness, and verify properties previously seen only in numerical calculations. The spectrum of the linearisation of the renormalisation operator at this fixed point is also explicitly determined. This strong coupling fixed point also helps describe the onset of a strange nonchaotic attractor in quasiperiodically forced systems.

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  • Science

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  • Mathematical Sciences

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276931 bytes

Publication date

2000

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This is a pre-print. The definitive version: MESTEL, B.D., OSBALDESTIN, A.H. and WINN, B., 2000. Golden mean renormalization for the Harper equation: The strong coupling fixed point. Journal of Mathematical Physics, 41(12), pp.8304-8330.

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