Related papers: Computing Chaotic Time-Averages from Few Periodic …
The flux-based statistical theory of the non-hierarchical three-body system predicts that the chaotic outcome distribution reduces to the chaotic emissivity function times a known function, the asymptotic flux. Here, we measure the chaotic…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
Because a chaotic zone can reduce the long timescale capture probabilities and cause catastrophic events such as close encounters with a planet or star during temporary capture, the dynamics of migrating planets is likely to be strongly…
Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime,…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes…
As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…