Related papers: Localized lasing modes of triangular organic micro…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
We show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing.
We introduce a new notion of stability for periodic orbits in polygonal billiards. We say that a periodic orbit of a polygonal billiard is $\lambda$-stable if there is a periodic orbit for the corresponding pinball billiard which converges…
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary, and also a circular scatterer in the interior of the disk. We investigate stability properties of some…
The paper describes a system of rays declining at small angles in lasers. The correlation between a group of rays and binomial coefficients is shown. The correlation of distribution of rays in the system of numbers placed in a…
Chirality is a fundamental concept in physics that underpins various phenomena in nonlinear optics, quantum physics, and topological photonics. Although the spin of a photon naturally brings chirality, orbital angular momentum can also…
We investigate chaotic scattering on an attractive step potential with a quadrupolar deformation. The phase space features of the bound billiard are studied by using the notion of symmetry lines to find periodic orbits. We show that the…
Gravitational microlensing events are powerful tools for the study of stellar populations. In particular, they can be used to discover and study a variety of binary systems. A large number of binary lenses have already been found through…
A periodic trajectory on a polygonal billiard table is stable if it persists under any sufficiently small perturbation of the table. It is a standard result that a periodic trajectory on an $n$-gon gives rise in a natural way to a closed…
We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly…
Periodic waves are standing wave solutions of nonlinear Schr\''odinger equations whose profile is periodic in space dimension one. We consider general nonlinearities and provide variational characterizations for the periodic wave profiles.…
In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…
We investigate the lasing modes in fully chaotic polymer microstadiums under optical pumping. The lasing modes are regularly spaced in frequency, and their amplitudes oscillate with frequency. Our numerical simulations reveal that the…
A multimode optical fiber with a truncated transverse cross section acts as a powerful versatile support to investigate the wave features of complex ray dynamics. In this paper, we concentrate on the case of a geometry inducing a mixed…
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
A simplified model of periodic chiral beam-lattices containing local resonators has been formulated to obtain a better understanding of the influence of the chirality and of the dynamic characteristics of the local resonators on the…
In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their…
The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case study with generic implications for…
New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in "Can the Elliptic Billiard Still Surprise Us?" (2020), Math. Intelligencer, 42(1): 6--17, some of which were…
The localization of waves in two-dimensional clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to find localized modes for…