Related papers: Combinatorial vs. classical dynamics: Recurrence
This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower…
We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…
We present a new method for generating robust guesses for unstable periodic orbits (UPOs) by post-processing turbulent data using dynamic mode decomposition (DMD). The approach relies on the identification of near-neutral, repeated…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
The behaviour of classical mechanical systems is characterised by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why…
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…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital…
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…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
From a simple analysis of particle orbits and fluid flows in presence or not of dissipation, some connections between apparently uncorrelated research areas are made. The main results point out for a deep relation between quantization of…
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated…
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…
A unified semiclassical framework is presented to describe the evaporative cooling of trapped atomic gases, accounting for both classical and quantum statistics. By combining global thermodynamics with phase-space distributions, general…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…