Related papers: Resonances and bifurcations in systems with ellipt…
We studied numerically electromagnetic response of the finite periodic structure consisting of the ${\cal{PT}}$ dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive…
The geometric resonance of open orbits in unidirectional lateral superlattices has been examined with high magnetic-field resolution. Magnetoresistance oscillations periodic in 1/B, analogous to the well-known commensurability oscillations…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the…
We consider the first order periodic systems perturbed by a $2N\ts 2N$ matrix-valued periodic potential on the real line. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the…
Spin-orbit coupling is often described in the "MacDonald torque" approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2,…
Observations of transversal coronal loop oscillations very often show the excitation and damping of oscillations in groups of coronal loops rather than in individual and isolated structures. We present results on the oscillatory properties…
Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic…
The simultaneous condensation of electronic and structural degrees of freedom gives rise to new states of matter, including superconductivity and charge-density-wave formation. When exciting such a condensed system, it is commonly assumed…
The high-order synchronization was studied in systems driven by external force and in autonomous systems with proper frequency mismatch. Differing from the literature, in this article, we demonstrate the occurrence of high-order (1:2)…
Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling…
Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio…
We demonstrate that a highly excited quantum electromagnetic mode strongly interacting with a single qubit exhibits several distinct resonances in addition to the Bloch-Siegert resonance condition that arises in the interaction with…
For area-preserving H\'enon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For constructing such perturbations, we use two methods, the…
Using bifurcation theory, we study the secular resonances induced by the Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depend only on the debris' orbital…
The amplification of disk oscillations resulting from nonlinear resonant couplings between the oscillations and a disk deformation is examined. The disk is geometrically thin and general relativistic with a non-rotating central source. A…