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Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem

Abstract

The Poincare surface-of-section analysis which the authors previously reported on the diamagnetic Kepler problem (classical hydrogen atom in a uniform magnetic field) in a transition region from regular to chaotic motions is simulated by an analytic means, by taking intersections of the energy integral and the approximate integral ..lambda.. of Solovev to obtain sections of the two separate regions of the motion that exist in the limit of a weak magnetic field (B ..-->.. 0). The origin of the unique hyperbolic point and the separatrix around which the onset of chaos takes place are thus identified. The invariant tori arising near the full chaos are shown to be simulated by this method but with modified parameter values in the expression ..lambda...
Authors:
Hasegawa, H; Harada, A; Okazaki, Y [1] 
  1. Kyoto Univ. (Japan). Dept. of Physics
Publication Date:
Nov 11, 1984
Product Type:
Journal Article
Reference Number:
AIX-16-025033; EDB-85-143177
Resource Relation:
Journal Name: J. Phys. A: Math. Gen.; (United Kingdom); Journal Volume: 17:11
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HYDROGEN; DIAMAGNETISM; ANALYTICAL SOLUTION; ATOMS; COMPUTER GRAPHICS; DYNAMICS; ENERGY; HAMILTONIANS; LIMITING VALUES; MAGNETIC FIELDS; MOTION; POINCARE GROUPS; SIMULATION; STOCHASTIC PROCESSES; ELEMENTS; LIE GROUPS; MAGNETISM; MATHEMATICAL OPERATORS; MECHANICS; NONMETALS; QUANTUM OPERATORS; SYMMETRY GROUPS; 640305* - Atomic, Molecular & Chemical Physics- Atomic & Molecular Theory- (-1987); 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
OSTI ID:
5350012
Country of Origin:
United Kingdom
Language:
English
Other Identifying Numbers:
Journal ID: CODEN: JPHAC
Submitting Site:
HEDB
Size:
Pages: L883-L888
Announcement Date:

Citation Formats

Hasegawa, H, Harada, A, and Okazaki, Y. Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem. United Kingdom: N. p., 1984. Web. doi:10.1088/0305-4470/17/16/005.
Hasegawa, H, Harada, A, & Okazaki, Y. Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem. United Kingdom. doi:10.1088/0305-4470/17/16/005.
Hasegawa, H, Harada, A, and Okazaki, Y. 1984. "Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem." United Kingdom. doi:10.1088/0305-4470/17/16/005. https://www.osti.gov/servlets/purl/10.1088/0305-4470/17/16/005.
@misc{etde_5350012,
title = {Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem}
author = {Hasegawa, H, Harada, A, and Okazaki, Y}
abstractNote = {The Poincare surface-of-section analysis which the authors previously reported on the diamagnetic Kepler problem (classical hydrogen atom in a uniform magnetic field) in a transition region from regular to chaotic motions is simulated by an analytic means, by taking intersections of the energy integral and the approximate integral ..lambda.. of Solovev to obtain sections of the two separate regions of the motion that exist in the limit of a weak magnetic field (B ..-->.. 0). The origin of the unique hyperbolic point and the separatrix around which the onset of chaos takes place are thus identified. The invariant tori arising near the full chaos are shown to be simulated by this method but with modified parameter values in the expression ..lambda...}
doi = {10.1088/0305-4470/17/16/005}
journal = {J. Phys. A: Math. Gen.; (United Kingdom)}
volume = {17:11}
journal type = {AC}
place = {United Kingdom}
year = {1984}
month = {Nov}
}