Related papers: Algebraic statistics of Poincar\'e recurrences in …
Hundred twenty years after the fundamental work of Poincar\'e, the statistics of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime,…
We analyze the statistical properties of Poincar\'e recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincar\'e…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal…
A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…
The Poincar\'e recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time. An analogous behavior occurs in certain quantum…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
For a probability measure preserving dynamical system $(\mathcal{X},f,\mu)$, the Poincar\'e Recurrence Theorem asserts that $\mu$-almost every orbit is recurrent with respect to its initial condition. This motivates study of the statistics…
The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
Understanding stickiness and power-law behavior of Poincar\'e recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees-of-freedom. We study such…
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…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
We study linear recurrences of Eulerian type of the form \[ P_n(v) = (\alpha(v)n+\gamma(v))P_{n-1}(v) +\beta(v)(1-v)P_{n-1}'(v)\qquad(n\ge1), \] with $P_0(v)$ given, where $\alpha(v), \beta(v)$ and $\gamma(v)$ are in most cases polynomials…
In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to power law behavior at asymptotic times. Time dependence of the survival probability of the…
We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…
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…
We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…
By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why…