Izvestiya of Saratov University.
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

dynamical chaos

Cascade of Invariant Curve Doubling Bifurcations and Quasi-Periodic Hénon Attractor in the Discrete Lorenz-84 Model

Background and Objectives: Chaotic behavior is one of the fundamental properties of nonlinear dynamical systems, including maps. Chaos can be most easily and reliably diagnosed using the largest Lyapunov exponent, which will be positive for the chaotic mode. Unlike flow dynamical systems, the presence of zero Lyapunov exponent in the spectrum is not an obligatory condition for maps. The zero exponent in the spectrum of a map will indicate the possibility of embedding such a map in a flow.

Dynamical Chaos In Quantum Systems

Complex dynamics of a quantum periodically driven square well is considered. It is shown that analysis of its ensemble average energy time series provides an identification of its dynamics to be either regular or chaotic. It has been found that enhancement of the driving force causes the energy spectrum to look like a spectrum of some random process, which may be identified as the signature of chaos in a quantum system. 

Cryptography from the Physicist's Point of View

The results of treating of crypto algorithms such as DES (USA) and GOST 28147-89 (Russia) with the help of nonlinear dynamics methods are presented. Point maps which are generated by the blocks of substitutions (S-blocks) are investigated. The phenomenon of return is demonstrated. The ergodicity of these maps are treated. An estimation of quality of S-block could be made by maps of first return. The results of statistical treating of S-biocks are presented.