Publication:
Bifurcations of Fibonacci generating functions

Date
2007-08
Authors
Özer, Mehmet
Cenys, Antanas
Polatoğlu, Yaşar
Hacıbekiroğlu, Gürsel
Akat, Ercüment
Valaristos, A.
Anagnostopoulos, A. N.
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PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
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Abstract

In this work the dynamic behaviour of the one-dimensional family of maps F-p,F-q(x) = 1/(1 - px - qx(2)) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean. (c) 2006 Elsevier Ltd. All rights reserved.

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Keywords
metallic means family , extended states , quasi-crystals , lattices , maps , transition , spectra , Trace , genişletilmiş devletler , Yarı-kristaller , parmaklıklar , haritalar , geçiş , spektrumlar , iz
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