Huimin Xie 1996 Nonlinearity 9 1469 doi:10.1088/0951-7715/9/6/005
Fibonacci sequences and homomorphisms of free submonoid for unimodal maps
Huimin Xie
Show affiliationsRecommended by P Grassberger
As a method of finding non-regular complexity in unimodal maps, an approach of Fibonacci sequences, i.e. by the operations of concatenation and cyclic shift of symbolic strings, is analysed rigorously. It turns out that all these kneading sequences obtained in this way can be seen as limits of two special kinds of homomorphisms of submonoids applied infinitely many times. A more general theorem of using homomorphisms of submonoid to obtain non-regular kneading sequences is proved. It contains the approach of Fibonacci sequences, the limits of period-doubling and period-n-tupling sequences, the 
-composition law and the generalized composition law as its special cases. Finally, some open questions are discussed.
- PACS
- MSC
- Subjects
- Dates
-
Issue 6 (November 1996)
Received 20 September 1995, in final form 6 June 1996
-
Fibonacci sequences and homomorphisms of free submonoid for unimodal maps
Huimin Xie 1996 Nonlinearity 9 1469
-
Quantum teleportation and entanglement swapping with linear optics logic gates
Christian Schmid et al 2009 New J. Phys. 11 033008
-
Multi-atom entanglement engineering and phase-covariant cloning via adiabatic passage
Shi-Biao Zheng 2005 J. Opt. B: Quantum Semiclass. Opt. 7 139
-
The theory of the ordinary Hall coefficient of iron at low temperatures
M G Cottam and R B Stinchcombe 1968 J. Phys. C: Solid State Phys. 1 1052
-
FOCUS ON TURBULENCE
Zellman Warhaft and Alain Pumir 2004 New J. Phys. 6
-
Interaction and propagation of waves in slotted waveguides
Yu V Shestopalov and N Z Kotik 2002 New J. Phys. 4 40
-
A novel subpixel edge detection system for dimension measurement and object localization using an analogue-based approach
M Baba and K Ohtani 2001 J. Opt. A: Pure Appl. Opt. 3 276
-
The Poincare limit in 2+1 dimensional quantum de Sitter gravity
L F Urrutia and F Zertuche 1992 Class. Quantum Grav. 9 641
-
Comparative study of different tip materials for surface modification by the scanning tunneling microscope
T Schaub et al 1992 Nanotechnology 3 77
-
Ultra-Scale Visualization: Research and Education
Kwan-Liu Ma et al 2007 J. Phys.: Conf. Ser. 78 012088
Related review articles
What's this?- Dimension of non-conformal repellers: a survey
- Progress in normal form theory
- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities