Related papers: Periodic Orbit Theory of Diffraction
Accurate and powerful analytic and computational methods developped by the author allow to obtain the highly non trivial total absorption spectrum of the Black Hole, as well as phase shifts and cross sections (elastic and inelastic), the…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
This paper presents a theoretical analysis of the recently reported observation of acoustic stop bands in two-dimensional scattering arrays (Robertson and Rudy, J. Acoust. Soc. Am. {\bf 104}, 694, 1998). A self-consistent wave scattering…
The aim of this work is to continue the analysis, started in arXiv:2105.02108, of the dynamics of a point-mass particle $P$ moving in a galaxy with an harmonic biaxial core, in whose center sits a Keplerian attractive center (e.g. a Black…
We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
After a short review of the principal theories of spiral structure in galaxies, I describe two new developments. First, it now seems clear that linear theory cannot yield a full description for the development of spiral patterns because…
We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur…
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…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and interacting with each other via elastic…
The low-frequency profiles of some pulsars manifest temporal broadening due to scattering, usually accompanied by flat polarization position angle (PA) curves. Assuming that the scattering works on the 4 Stokes parameters in the same way,…
Using time-independent scattering matrices, we study how the effects of nonclassical paths on the recurrence spectra of diamagnetic atoms can be extracted from purely quantal calculations. This study reveals an intimate relationship between…
This work applies Mie scattering theory to provide a new perspective on the propagation of light through a spherical obstacle, offering a novel explanation for the formation of the Poisson spot (also known as the Arago or Fresnel spot). We…
[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix elements as well. The derivation of the…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…