Bounded Gain of Energy on the Breathing Circle Billiard
نویسندگان
چکیده
The Breathing Circle is a 2-dimensional generalization of the Fermi Accelerator. It is shown that the billiard map associated to this model has invariant curves in phase space, implying that any particle will have bounded gain of energy.
منابع مشابه
Determination of Gain and Phase Margins in Lur’e Nonlinear Systems using Extended Circle Criterion
Nonlinearity is one of the main behaviors of systems in the real world. Therefore, it seems necessary to introduce a method to determine the stability margin of these systems. Although the gain and phase margins are established criteria for the analysis of linear systems, finding a specific way to determine the true value of these margins in nonlinear systems in general is an ongoing research i...
متن کاملExpansion method for stationary states of quantum billiards
A simple expansion method for numerically calculating the energy levels and the corresponding wave functions of a quantum particle in a two-dimensional infinite potential well with arbitrary shape ~quantum billiard! is presented. The method permits the study of quantum billiards in an introductory quantum mechanics course. According to the method, wave functions inside the billiard are expresse...
متن کاملOn configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards
The classical billiard system describes the motion of a point in a plane domain subject to the elastic reflection off the boundary, described by the familiar law of geometrical optics: the angle of incidence equals the angle of reflection; see, e.g., [13, 14] for surveys of mathematical billiards. For every n ≥ 2, the billiard system inside a circle has a very special property: every point of t...
متن کاملIrregular Scattering of Particles Confined to Ring-Bounded Cavities
The classical motion of a Ii"ee particle that scatters elastically from ring-bounded cavities is analyzed nunaerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed of N scatrefers the Ilow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically with N, which is consistent with the theoretica...
متن کاملDual billiards in the hyperbolic plane*
We study an area preserving map of the exterior of a smooth convex curve in the hyperbolic plane, defined by a natural geometrical construction and called the dual billiard map. We consider two problems: stability and the area spectrum. The dual billiard map is called stable if all its orbits are bounded. We show that both stable and unstable behaviours may occur. If the map at infinity has a h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008