[en] Development and introduction of nanotechnologies in the oil industry is one of the most pressing issues of the present times.For the first time in the world practice scientific-methodological basis and application practice of nanotechnologies in oil industry is developed on the basis of uniform, scientifically proven approach by taking into account the specificities of oil and gas industry.The application system of such nanotechnologies was developed in oil and gas production.Mathematical models of nanotechnological processes, i.e.^chaos regulation^and hyper-accidental process were offered. Nanomedium and nanoimpact on the ^well-layer^system was studied. Wide application results of nanotechnologies in SOCAR's production fields in oil and gas production are shown.Research results of ^NANOSAA^on the basis of ^NANO + NANO^effect are described in the development.For the first time in world practice ^NANOOIL^,NANOBITUMEN^,NANOGUDRON' and ^NANOMAY' systems on the basis of machine waste oil in the drilling mud were developed for the application in oil and gas drilling. Original property, ^effect of super small concentrations^and ⁿanomemoryⁱn ^NANOOIL^and ^NANOBITUMEN^systems was discovered.By applying ^NANOOIL^,NANOBITUMEN^and ^NANOMAY^systems in the drilling process was discovered: the increase of linear speed, early turbulence, decrease of hydraulic resistance coefficient and economy in energy consumption.Hyper-accidental evaluation of mathematical expectation of general sum of values of the surface strain on the sample data is spelled out with the various experiment conditions. Estimated hyper-accidental value of the mathematical expectation allows us to offer practical recommendations for the development of new nanotechnologies on the basis of rheological parameters of oil.

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[en] One studied a complex dynamics of the mock-up of a two-resonant klystron generator with delayed feedback. One analyzed theoretically the self-excitation conditions and the generation stationary regimes. Paper presents the numerical simulation results of the self-modulation and the chaotic regimes and studied in detail the scenarios of transition to chaos in the centre and near the boundary of the generation regimes. One discusses the effect of space charge forces on generator dynamics

[en] The paper deals with the problem of dividing the trend and the chaotic component of chaotic time series in the absence of information about the characteristics of the chaotic component. This kind of problem arises in solving problems in nuclear physics, biomedicine, and many other applied problems. The scheme consists of two stages. At the first stage, using smoothing linear splines for different values of the smoothing parameter, the 'trend component' is highlighted. At the second stage, using the method of least squares, an unknown dispersion σ² of the noise component is found.

[en] A number of new dynamic systems, interesting to the applications is considered, for which presence the small perturbation results in essential change of their dynamics.

[en] The results of the study of smooth Hamiltonian systems with a piecewise linear force, which are used for finding the invariant curves of standard mapping, are presented. Conditions of the global chaos in two-dimensional canonical mapping are discussed. It has been found that at certain values of perturbation parameter unsplit separatrices of integer and fractional resonances arise among global invariant curves. Numerical and analytical results that directly or indirectly concern the effect of separatrix persistence in the absence of attendant dynamic chaos are analyzed

[en] Below is a review of the results of theoretical and numerical studies of the special part that low-frequency secondary harmonics occurring in sum and in difference of the fundamental frequencies being a part of the Hamiltonian may play in the nonlinear Hamiltonian systems. A pendulum the perturbation of which is represented in the Hamiltonian by two asymmetrical harmonics with high and module close frequencies is used as an example. One derived analytical expression of the secondary harmonic contribution into amplitude of separatrix representation of the mentioned system and used the mentioned expression to study the case of rather low secondary frequencies ignored previously. One specifies the regions where amplitude of the separatrix representation increases linearly with frequency, while the dimensions of the chaotic layer does not depend on it. One presents the comparison of theoretical and numerical study results

[en] The pervious study on the family of the smooth constant and discrete two-parametric Hamiltonian systems with the piecewise force is continued. It is established that the dependence of the Melnikov-Arnold integral for such systems on the frequency is exponential and oscillatory. It is shown that by the presence of two different perturbation frequencies the secondary harmonics originating on their sum may provide for the basic contribution to the chaotic layer formation. The areas of special values of the perturbation parameter are found, whereby under the conditions of the strong local chaos, the upper separatrix of the fractional resonance remains preserved whereas the lower one becomes distorted and vice versa

[en] The approach, making it possible to connect the effect of the quantum compression and classic instability by means of establishing the evolution equations for the dispersion matrix elements, which directly include the stability matrix elements, is proposed. The solution of these equations is registered through the evolution operator, the knowledge whereof makes it possible to analyze the system instability at the finite times. Two physical systems: the parametric degenerated and nondegenerated amplifiers with the δ-shaped jerks are studied on the basis of the developed formalism

[en] One of the main models used to study problems of ferromagnetic resonance is the Landau-Lifshitz phenomenological model. According to this model, the dynamics of the magnetization in a ferromagnet is described by a nonlinear Landau-Lifshitz equation. Because of the nonlinearity of this equation the physical properties described by it are extremely diverse. Depending on the physical situation, a system is characterized by soliton or chaotic solutions. Usually it is assumed that a necessary condition for obtaining a chaotic solution is that the system be acted upon by a random field due to fluctuations of the local magnetization. It is shown here that chaotic dynamics can also be obtained in the case of a regular external force. The conditions for the appearance of Hamiltonian chaos are determined, and numerical estimates are made for concrete substances. A kinetic equation describing the dynamics of the magnetization under conditions of stochasticity is obtained. It is shown that the solution of the kinetic equation agrees well with the solutions of the Landau-Lifshitz equation, confirming the applicability of the mathematical description for chaotic dynamical systems