Related papers: Stationary phase methods and the splitting of sepa…
We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We…
A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general…
We study the dynamics of an Atomic Force Microscope (AFM) model, under the Lennard-Jones force with non-linear damping, and harmonic forcing. We establish the bifurcation diagrams for equilibria in a conservative system. Particularly, we…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…
We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and…
We study the existence of real-analytic first integrals and real-analytic integrability for perturbations of integrable systems in the sense of Bogoyavlenskij including non-Hamiltonian ones. We especially assume that there exists a family…
The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P,…
A rigid body in an ideal fluid is an important example of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(3) = so(3)\ltimes\mathbb R^3$. We present the bi-Hamiltonian structure and the corresponding variables of…
The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the…
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…
Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the…
We consider a particular class of equations of motion, generalizing to n degrees of freedom the "dissipative spin--orbit problem", commonly studied in Celestial Mechanics. Those equations are formulated in a pseudo-Hamiltonian framework…
We consider an inverted harmonic oscillator in the space $L^{2} (\mathbb{S})$ of square-integrable functions on the circle $\mathbb{S}$ and compute its density of states employing the stationary phase approximation. Our computation is based…
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the…