Related papers: On iterating operators and on generalized periodic…
Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their…
We reconsider the classical problem of the continuation of degenerate periodic orbits in Hamiltonian systems. In particular we focus on periodic orbits that arise from the breaking of a completely resonant maximal torus. We here propose a…
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…
The notion of phase plays an esential role in both classical and quantum mechanics.But what is a phase? We show that if we define the notion of phase in phase (!) space one can very easily and naturally recover the Heisenberg-Weyl…
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario…
A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
Permanental processes can be viewed as a generalisation of squared centered Gaussian processes. We develop in this paper two main subjects. The first one analyses the connections of these processes with the local times of general Markov…
A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered.…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…