Bifurcations of Fibonacci generating functions - Özer, Mehmet; Cenys, Antanas; Hacıbekiroğlu, Gürsel; Akat, Ercüment; Valaristos, A.; Anagnostopoulos, A. N.; POLATOĞLU, YAŞAR (PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND, 2007)
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.
Keywords: metallic means family; extended states; quasi-crystals; lattices; maps; transition; spectra; Trace; genişletilmiş devletler; Yarı-kristaller; parmaklıklar; haritalar; geçiş; spektrumlar; iz