Related papers: Probing a regular orbit with spectral dynamics
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Tremendous progress has been made recently in modelling the morphology and kinematics of centers of galaxies. Increasingly realistic models are built for central bar, bulge, nucleus and black hole of galaxies, including our own. The newly…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
We calculate stationary configurations of rapidly rotating compact stars in general relativity, to study the properties of circular orbits of test particles in the equatorial plane. We search for simple, but precise, analytical formulae for…
Many approaches to galaxy dynamics assume that the gravitational potential is simple and the distribution function is time-invariant. Under these assumptions there are traditional tools for inferring potential parameters given observations…
The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity $\Delta_3(L)$, which is a measure for the correlations between the eigenvalues, decreases to quite…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
This paper presents a new approach to studying galactic structures. They are considered as the low-frequency normal modes in a disc of orbits precessing at different angular speeds. Such a concept is an adequate alternative to the commonly…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…