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...

For 0 < λ < 1/e the Julia set of λez is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpińska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a qu...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...

In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen’s theorem that cusps are dense on the Bers’ boundary of Teichmüller...

in this research prediction methods of artificial neural network and chaos theory are employed to predict daily, weekly and monthly runoff. for this, runoff series data observed at pole-kohneh located in the qareh-soo river. the nonlinear predictions of chaos are found to be in close agreement with the observed runoff, with high correlation coefficient for daily and weekly time scales. predicte...

Delvenne, Kůrka and Blondel have defined new notions of computational complexity for arbitrary symbolic systems, and shown examples of effective systems that are computationally universal in this sense. The notion is defined in terms of the trace function of the system, and aims to capture its dynamics. We present a Devaney-chaotic reversible cellular automaton that is universal in their sense,...

In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic behavior in the meaning of Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustration example is detailed in ...

Ferlito A, Devaney KO, Rinaldo A, et al. Ear cholesteatoma versus cholesterol granuloma. Ann Otol Rhinol Laryngol 1997;106:79–85 This is an excellent histopathology-based review (no images) that defines and differentiates these two entities. Very interesting information. Authors reiterate that cholesteatoma is a misnomer: it is not a neoplasm (-oma), there are no cholesterol crystals (chole-), ...