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We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an…

We address the time decay of the Loschmidt echo, measuring sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using semiclassical analysis, we show that the Loschmidt echo may exhibit…

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…

In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…

We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…

We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…

We present a detailed numerical study of finite volume effects for masses and decay constants of the octet of pseudoscalar mesons. For this analysis we use chiral perturbation theory and asymptotic formulae a la Luscher and propose an…

We analyze the structure and stickiness in the chaotic components of generic Hamiltonian systems with divided phase space. Following the method proposed recently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)], the sticky regions are…

We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable recurrence time. We show that the decay of correlations of the SRB…

This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…

Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, can estimate these finite-time effects. For the first time, exact…

We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the…

Excitable media can develop spiral chaos, in which the number of spirals changes chaotically with time. Depending on parameter values in dynamical equations, spiral chaos may permanently persist or spontaneously arrive at a steady state…

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a…