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Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field which is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…
The rotation rate of a star has important implications for the detectability, characterisation and stability of any planets that may be orbiting it. This chapter gives a brief overview of stellar rotation before describing the methods used…
In an effort to better understand the formation and evolution of barred galaxies, we have examined the properties of equatorial orbits in the effective potential of one model of a rapidly rotating, steady-state gas-dynamical bar that has…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
We present a general theory of multiorbital spin waves in magnetically ordered metallic systems. Motivated by the itinerant magnetism of iron-based superconductors, we compare the magnetic excitations for two different scenarios: when the…
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions…
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a…
In our Solar system, spin-orbit coupling is a common phenomenon in binary asteroid systems, where the mutual orbits are no longer invariant due to exchange of angular momentum between translation and rotation. In this work, dynamical…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
All circumbinary planets (CBPs) currently detected are located in almost co-planar configurations with respect to the binary orbit, due to the fact that CBPs with higher misalignment are more difficult to detect. However, observations of…
Superexchange calculation is performed for multi-orbital band models with broken inversion symmetry. Orbital-changing hopping terms allowed by the symmetry breaking electric field lead to a new kind of orbital exchange term closely…
The trajectories of a qubit dynamics over the two-sphere are shown to be geodesics of certain Riemannian or physically-sound Lorentzian manifolds, both in the non-dissipative and dissipative formalisms, when using action-angle variables.…
The chiral geometry of the multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters $\gamma$ in the particle rotor model with $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$. The energy…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
X-structures are often observed in galaxies hosting the so-called B/PS (boxy/peanuts) bulges and are visible from the edge-on view. They are the most notable features of B/PS bulges and appear as four rays protruding from the disk of the…