Related papers: Resonances and bifurcations in systems with ellipt…
We study the dynamics of the space debris in the 1:1 and 2:1 resonances, where geosynchronous and GPS satellites are located. By using Hamiltonian formalism, we consider a model including the geopotential contribution for which we compute…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Systems of ODEs coupled with the topology of a closed ring are common models in biology, robotics, electrical engineering, and many other areas of science. When the component systems and couplings are identical, the system has a cyclic…
We consider the resonant system of amplitude equations for the conformally invariant cubic wave equation on the three-sphere. Using the local bifurcation theory, we characterize all stationary states that bifurcate from the first two…
Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their…
We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A…
A unified framework is proposed to quantitatively characterize pitchfork bifurcations and associated symmetry breaking in the elliptic restricted three-body problem (ERTBP). It is known that planar/vertical Lyapunov orbits and Lissajous…
Permanently deformed objects in binary systems can experience complex rotation evolution, arising from the extensively studied effect of spin-orbit coupling as well as more nuanced dynamics arising from spin-spin interactions. The ability…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
We study the dynamics of the space debris in regions corresponding to minor resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2, 5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
Convection in a cylindrical container of small aspect ratio is studied. It is known that when, in addition to buoyancy forces, thermocapillarity effects are taken into account, resonant interactions of two modes may appear. In the case of…
We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions…
We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known "frown-smile" side-on morphology, is…
The time-periodic scalar delay differential equation $\dot x(t)=\gamma f(t,x(t-1))$ is considered, which leads to a resonant bifurcation of the equilibrium at critical values of the parameter. Using Floquet theory, spectral projection and…
The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law.…
We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical…