منابع مشابه
Are There Chaotic Tilings ?
We develop a class of examples in the form of tiling dynamical systems for use as toy models in statistical mechanics, to analyze the possible existence of disordered crystals. We give the first such models which are disordered in the sense of having no discrete spectrum. * Research supported in part by a grant from the Israel Science and Technology Ministry ** Research supported in part by NSF...
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In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of R , whose most familiar example is provided by the N−dimensional torus T . It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaossynchronization mechanis...
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In this article we initiate the use of noncommutative geometry in the theory of dynamical systems. After investigating by examples the unusual and striking elementary properties of the Penrose tilings and the Arnold cat map, we associate a finite symbolic dynamics with finite grammar rules to each of them. Instead of studying these Markovian systems with the help of set-topology, which would gi...
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Chaos synchronization has exhibited an increasing interest in the last decade since the pioneering works reported in (Pecora & Carroll, 1990; Pecora & Carroll, 1991), and it has been advocated as a powerful tool in secure communication (Blekhman et al, 2002; Kolumban et al,1998; Nijmeijer, 1997; Kennedy & Ogorzalek, 1997). Chaotic systems are indeed characterized by a great sensitivity to the i...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1993
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02098297