Related papers: Dynamics near the p : -q Resonance
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
Using a probabilistic approach we study the parallel dynamics of fully connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown to exist at zero temperature. A recursive scheme is set up to determine the time…
We study dynamical evolution of a resonant triple system formed by an inner EMRI and an additional outer MBH. The relevant resonant state (\lambda_2-\varpi_1 ~ const) is supported by the relativistic apsidal precession of the inner EMRI,…
If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the…
A new method of deriving reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a set of resolved variables that define a model reduction, the quasi-equilibrium…
The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$, $0\leq \mu \leq 1/2$, that circle each other with period equal to $2\pi$. When…
We consider the classical response of a strongly chaotic Hamiltonian system. The spectrum of such a system consists of discrete complex Ruelle-Pollicott (RP) resonances which manifest themselves in the behavior of the correlation and…
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…
We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and…
We study the time correlation functions of coupled linear Langevin dynamics without and with inertia effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three…
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…
We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex…
Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to…
An exactly soluble non-linear interaction Hamiltonian is proposed to study fundamental properties of the entanglement dynamics for a coupled non-linear oscillators. The time-evolved state is obtained analytically for initial products of two…
The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly non-trivial when the ground states…
Recently, it has been reported the discovery of a dense ring around the trans-Neptunian object 50000 Quaoar. The ring particles seem to be very close to the 6/1 mean motion resonance with Weywot, the only known satellite in the system. In…
We study numerically and analytically isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). The probability of finding the initial state in time, the so-called fidelity, decays fastest for…
The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1:1 (saddle-centre) and 1:2 (period-doubling). The twist, which is the derivative of the rotation number…