Related papers: Chaotic Maps, Hamiltonian Flows, and Holographic M…

We present a method to control transport in Hamiltonian systems. We provide an algorithm - based on a perturbation of the original Hamiltonian localized in phase space - to design small control terms that are able to create isolated…

In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…

Cloaking is a method of making obstacles undetectable. Here we cloak unit cells of a magnetic pattern squeezed into an otherwise periodic pattern from a magnetically driven colloidal flow. We apply a time-periodic external magnetic field…

Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly…

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…

Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they…

We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…

We investigate the properties of motion in a map model derived from a galactic Hamiltonian made up of perturbed elliptic oscillators. The phase space portrait is obtained in all three different cases using the map and numerical integration…

We obtain stationary transport in a Hamiltonian system with ac driving in the presence of a dc bias. A particle in a periodic potential under the influence of a time-periodic field possesses a mixed phase space with regular and chaotic…

Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…

In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly…

Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result,…

Special subsets of orbits in chaotic systems, e.g. periodic orbits, heteroclinic orbits, closed orbits, can be considered as skeletons or scaffolds upon which the full dynamics of the system is built. In particular, as demonstrated in…

In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…

Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…

A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms…

We consider a linear-quadratic deterministic optimal control problem where the control takes values in a two-dimensional simplex. The phase portrait of the optimal synthesis contains second-order singular extremals and exhibits modes of…