相关论文: Phase-Space Volume of Regions of Trapped Motion: M…
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
We show that stable double-frequency orbits form the backbone of double bars, because they trap around themselves regular orbits, as stable closed periodic orbits do in single bars, and in both cases the trapped orbits occupy similar volume…
A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work…
Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured…
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 dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the…
We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
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…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
The two-to-two four-dimensional scattering amplitude of identical scalars obeys rigorous two-sided non-perturbative bounds derived via the modern numerical S-matrix bootstrap. These bounds carve out an allowed region with a rich boundary…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
Via evaluation of the Lyapunov exponent, we report the discovery of three prominent sets of phase space regimes of quasi-periodic orbits of charged particles trapped in a dipole magnetic field. Besides the low energy regime that has been…
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic…
The statistics of Poincar\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this…