• Corpus ID: 56096505

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

@inproceedings{Mestel2000GoldenMR,
  title={Golden mean renormalization for a generalized Harper equation: The strong coupling fixed point},
  author={Ben Mestel and Andrew H. Osbaldestin},
  year={2000}
}
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… 

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References

SHOWING 1-10 OF 11 REFERENCES
Renormalization approach to quasiperiodic quantum spin chains
Renormalization-group analysis of the discrete quasiperiodic Schrödinger equation
Recently developed scaling concepts in the theory of quasiperiodic dynamical systems are used to develop an exact renormalization group applicable to the discrete, quasiperiodic Schrodinger equation.
Renormalization of correlations and spectra of a strange non-chaotic attractor
We study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum. We show that the symbolic dynamics is exactly described by a language
Universal criterion for the breakup of invariant tori in dissipative systems.
  • Ketoja
  • Physics
    Physical review letters
  • 1992
TLDR
Numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments, and is argued that the (minimal) slope of the critical iterated circle map is proportional to the effective Jacobian determinant.
Iterative Functional Equations
Preface Symbols and conventions 1. Introduction 2. Iteration 3. Linear equations and branching processes 4. Regularity of solutions of linear equations 5. Analytic and integrable solutions of linear
Birth of a strange nonchaotic attractor: A renormalization group analysis.
  • Kuznetsov, Pikovsky, Feudel
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
Periodic Orbits of Renormalisation of the . . .
  • Physics
  • 2000
Correlation properties of a quasiperiodically forced two-level system.
  • Feudel, Pikovsky, Zaks
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
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