Related papers: Resonances for homoclinic trapped sets
Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in…
We propose theoretically a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, $C_6$, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the…
We experimentally realize a highly tunable superfluid oscillator circuit in a quantum gas of ultracold atoms and develop and verify a simple lumped-element description of this circuit. At low oscillator currents, we demonstrate that the…
We consider a pair of atoms in an arbitrary trapping potential in the presence of magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states taking into account possible coupling between…
We consider the Lam\'e transmission problem in $\mathbb{R}^3$ with a bounded isotropic elastic inclusion in a high-contrast setting, where the interior-to-exterior Lam\'e moduli and densities scale like $1/\tau$ as $\tau\to0$. We study the…
When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one…
We use three-dimensional simulations to study the statistics of supersonic turbulence in molecular clouds. Our numerical experiments describe driven turbulent flows with an isothermal equation of state, Mach numbers around 10, and various…
The existence and bifurcation of homoclinic orbits in planar piecewise linear homogeneous systems with two regions separated by a discontinuity boundary are investigated in this paper. In addition, existence of periodic orbits and stability…
In this paper, we study the semi-classical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvature. Assuming that there is a strip without resonances below…
We find that hexagonal structures forming in semiconductor resonators can range from coherent patterns to arrangements of loosely bound spatial solitons, which can be individually switched. Such incoherent arrangements are stabilized by…
Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is…
We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term…
We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection…
Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant…
The unique properties of topological semimetals have strongly driven efforts to seek for new topological phases and related materials. Here, we identify a critical condition for the existence of linked nodal rings (LNRs) in symmorphic…
The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
We present two results concerning the spin (or pseudo spin) dynamics of trapped quantum gases in the hydrodynamic regime described by the Leggett equations. First, we apply perturbation theory to extend the ``bounded diffusion'' description…
We construct symplectomorphisms in dimension $d\geq 4$ having a semi-local robustly transitive partially hyperbolic set containing $C^2$-robust homoclinic tangencies of any codimension $c$ with $0<c\leq d/2$.
Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of…