相关论文: Integral representations of periodic and cyclic fr…

A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…

We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…

We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and…

In this paper, we investigate traces of cycle integrals of certain meromorphic modular forms. By relating them to regularised theta lifts we provide explicit formulae for them in terms of coefficients of harmonic Maass forms.

We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin…

We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…

A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional…

This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…

The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…

We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time…

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a…

We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…

We show that if a random variable is the final value of an adapted log-H\"{o}lder continuous process, then it can be represented as a stochastic integral with respect to a fractional Brownian motion with adapted integrand. In order to…

We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

It is proved that the mean signature of multi-dimensional fractional brownian motion admits a meromorphic continuation in the hurst parameter to the entire complex plane. Each contstituent mean iterated integral is a sum of hypergeometric…