Zagazig University Digital Repository
Home
Thesis & Publications
All Contents
Publications
Thesis
Graduation Projects
Research Area
Research Area Reports
Search by Research Area
Universities Thesis
ACADEMIC Links
ACADEMIC RESEARCH
Zagazig University Authors
Africa Research Statistics
Google Scholar
Research Gate
Researcher ID
CrossRef
STOCHASTIC-TRANSITION OF FREE MOTION IN BILLIARDS WITH BORDERS GIVEN BY EQUIPOTENTIAL LINES OF THE DIAMAGNETIC KEPLER-PROBLEM
Faculty
Science
Year:
1992
Type of Publication:
Article
Pages:
7424-7430
Authors:
ABULMAGD, AY, MULLER, K
DOI:
10.1103/PhysRevA.46.7424
Journal:
PHYSICAL REVIEW A AMERICAN PHYSICAL SOC
Volume:
46
Research Area:
Optics; Physics
ISSN
ISI:A1992KE87100015
Keywords :
STOCHASTIC-TRANSITION , FREE MOTION , BILLIARDS WITH BORDERS
Abstract:
We compare the transition from ordered to chaotic motion in a potential with that in a billiard, whose borders are defined by the maximal equipotential line of the potential system in the case of hydrogen in a uniform magnetic field. For the billiard we calculate the Poincare maps, the fraction of regular motion on the surface of section, and the stability properties of the shortest periodic orbits. In contrast to the H atom, the billiard shows a generic transition to chaos. While the shape of the orbits is determined by the boundary and is thus very similar, their properties of stability are different: The potential tends to stabilize the motion. The onset of instability in the billiard can be understood in terms of the curvature of the boundary; for the potential system the Gaussian curvature of the potential-energy surface is shown to be the relevant parameter.
Online
PDF
جامعة المنصورة
جامعة الاسكندرية
جامعة القاهرة
جامعة سوهاج
جامعة الفيوم
جامعة بنها
جامعة دمياط
جامعة بورسعيد
جامعة حلوان
جامعة السويس
شراقوة
جامعة المنيا
جامعة دمنهور
جامعة المنوفية
جامعة أسوان
جامعة جنوب الوادى
جامعة قناة السويس
جامعة عين شمس
جامعة أسيوط
جامعة كفر الشيخ
جامعة السادات
جامعة طنطا
جامعة بنى سويف