ISSN 0869-6632 (Online)
ISSN 2542-1905 (Print)

Review of Actual Problems of Nonlinear Dynamics

Multifractal analysis of digital images

The article is based on the lecture that was given by the first author at the school StatInfo­2009. In the first part the microcanonical variant of multifractal formalism is reviewed. Possibilities for digital image analysis and reconstruction are discussed at the level of technical strictness.

Theory of waveguides excitation

The theory of waveguide excitation is presented, based on expansions of the electromagnetic ?eld by proper waves of waveguide. Necessary properties of smooth and periodic waveguides, including the conditions of orthogonality of plane and the volume of the waveguide are given. Main properties of pseudo-periodic waveguides are described. Thisis a new class of waveguide systems. Di?erent forms of the waveguides-excitation theory are considered.

Development and improvement of field emitters containing carbon materials

Achievements and problems in creation of ?eld emitters for vacuum microwave devices are described. The main attention is devoted to the emitters made of containing carbon materials for  high-voltage devices operating at technical vacuum conditions 10?6–10?8 Torr. The brief review of existing works is presented. Results of investigations performed in SPbSPU are described.

Unique properties of open cavities and wavegiudes containing layered metamaterial

The review of works on studying arti?cial media with negative refractive index and  their unique application is given. We make a point of negative refraction and lens e?ects in plan-parallel  layers of such metamaterials. The properties and stability conditions of waveguide modes in  layered structures and open cavities are considered in terms of the e?ective di?raction and  dispersion lengths.

Stochastic bifurcations

The modern knowledges of bifurcations of dynamical systems in the presence of noise are presenred. The main definitions are given and certain typical examples of the bifurcations in the presence of additive and multiplicative noise are considered.

Vacuum particle creation in strong fields: statistical aspects

In the present review we summarize the known informations about the evolution of a strongly nonequilibrium quasiparticle electron­positron plasma created from the vacuum under the influence of a strong nonstationary electromagnetic field. The methodical basis is given by quantum kinetic equations of the non­Markovian type which are nonperturbative consequences of the basic equations of QED in the collisionless approximation.

Longitudinal coherence of optical field

Spatial coherence of an optical field in a direction of its propagation depending on parameters of frequency and angular spectra of the field is considered. The expressions for function and length of longitudinal coherence are derived depending on width of frequency and angular spectra. The competing influence of angular and frequency spectra of a field on its longitudinal coherence is discussed. The experimental study with use the Michelson interferometer of longitudinal shift confirming theoretical results are executed.

Distribution of the laminar phases in the case of type­i intermittency with noise

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

Chaos and nonintegrability in hamiltonian systems

The article is devoted to historical development of one key aspect of Hamiltonian systems – nonintegrability, and its relation with chaotic behavior of the system. Evolution from the concept of quite integrable system to partly integrable one is shown. The relation of nonintegrability with such fundamental concepts as Kolmogorov stability, systems with divided phase space, Arnold di?usion, Zaslavsky web and others is discussed.

Autonomous systems with quasiperiodic dynamics examples and their properties: review

The paper is a review of well-known in nonlinear dynamics models with low dimensional of phase space and quasiperiodic behavior. Also new results related to analysis of many-frequencies quasiperiodic oscillations for models with external action and coupled oscillators are discussed. Download full version