‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

We define here e-chaos and study its interrelationships with P -chaos and Ruelle-Takens chaos. We show that a continuous self map f on a compact metric space is e-chaotic (P -chaotic) need not imply the induced map f̄ : K(X) → K(X) is e-chaotic (P -chaotic) and vice-versa, where K(X) is the space of all non-empty compact subsets of X endowed with Hausdorff metric. Mathematics Subject Classificat...

This chapter provides an overview of the state of the art of current chaos communication schemes and introduces the use of signal processing to improve the communication performances. Popular communication schemes in the literature, including chaotic spreading sequence (CSS), chaotic carrier (CC), chaos masking (CM), chaos shift keying (CSK), differential chaos shift keying (DCSK) and chaotic p...

A numerical study has been done of collisions between protons and hydrogen atoms, treated as classical particles, at low impact velocities. The presence of chaos has been looked for by investigating the processes with standard techniques of the chaotic–scattering theory. The evidence of a sharp transition from nearly regular scattering to fully developed chaos has been found at the lower veloci...

Vitamin E seems to have practically become a standard among my patients. This week I heard Dr. Zorba Paster endorse its use during his popular call-in public radio talk show, Zorba Paster on Your Health. A wellness newsletter from the University of California at Berkeley and academic cardiologists at continuing medical education presentations have encouraged its use. The New England Journal of ...

With the popularity and development of the Internet, E-commerce gradually spearhead the international trade, and become the main medium of trade. The application and development of E-commerce poses a severe challenge toward the traditional legal system, and bring about lots of new legal problems, especially worrisome is the evidence of E-commerce, which constitutes the major stumbling blocks in...

Chaos synchronization in some dynamical systems is studied in a general case. We use the boundedness of some dynamical systems, nonreplica approach to chaos synchronization and Routh-Hurwitz criteria to propose a simple method to make negative all the conditional Lyapunov exponents. The method is tested on the classical Lorenz model and one of Rossler models. Generalization of some features of ...

Chaos in Robertson-Walker cosmological models where gravity is coupled to one or more scalar fields has been studied by a few authors, mostly using numerical simulations. In this paper we begin a systematic study of the analytical aspect. We consider one conformally coupled scalar field and, using the fact that the model is integrable when the field is massless, we show in detail how homoclinic...

We consider the semiclassical approximation to the spectral form factor K(τ) for twodimensional uniformly hyperbolic systems, and derive the first off-diagonal correction for small τ . The result agrees with the τ -term of the form factor for the GOE random matrix ensemble. PACS numbers: 03.65.Sq Semiclassical theories and applications. 05.45.Mt Semiclassical chaos (“quantum chaos”). 1 E-mail: ...