Global flow of the anisotropic Kepler problem on negative energy levels when?>9/8

1987 ◽  
Vol 38 (1) ◽  
pp. 21-45
Author(s):  
J. Casasayas
Keyword(s):  
Kepler Problem ◽  
Energy Levels ◽  
Negative Energy ◽  
Global Flow ◽  
Anisotropic Kepler Problem

scholarly journals Symmetric Periodic Orbits in the Anisotropic Kepler Problem

1983 ◽  
Vol 74 ◽  
pp. 263-270
Author(s):  
Josefina Casasaya ◽  
Jaume Llibre
Keyword(s):  
Energy Level ◽  
Periodic Orbits ◽  
Kepler Problem ◽  
Negative Energy ◽  
Velocity Curve ◽  
Zero Velocity ◽  
Anisotropic Kepler Problem ◽  
Symmetric Periodic Orbits ◽  
Group Of Symmetries

AbstractThe anisotropic Kepler problem has a group of symmetries with three generators; they are symmetries respect to zero velocity curve and the two axes of motion’s plane. For a fixed negative energy level it has four homothetic orbits. We describe the symmetric periodic orbits near these homothetic orbits. Full details and proofs will appear elsewhere (Casasayas-Llibre).

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

scholarly journals Classical and Quantum Correspondence in Anisotropic Kepler Problem

10.5772/55208 ◽  
2013 ◽  
Author(s):  
Keita Sumiya ◽  
Hisakazu Uchiyama ◽  
Kazuhiro Kubo ◽  
Tokuzo Shim
Keyword(s):  
Kepler Problem ◽  
Anisotropic Kepler Problem ◽  
Quantum Correspondence

Efficient quantisation scheme for the anisotropic Kepler problem

1987 ◽  
Vol 20 (15) ◽  
pp. L965-L968 ◽  
Author(s):  
D Wintgen ◽  
H Marxer ◽  
J S Briggs
Keyword(s):  
Kepler Problem ◽  
Anisotropic Kepler Problem

Orbit systematics in anisotropic Kepler problem

2008 ◽  
Vol 13 (1) ◽  
pp. 218-222
Author(s):  
Kazuhiro Kubo ◽  
Tokuzo Shimada
Keyword(s):  
Kepler Problem ◽  
Anisotropic Kepler Problem

scholarly journals ON THE STABILITY OF COHERENT STATES FOR PAIS–UHLENBECK OSCILLATOR

2013 ◽  
Vol 28 (12) ◽  
pp. 1350038 ◽  
Author(s):  
SOUVIK PRAMANIK ◽  
SUBIR GHOSH
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Energy Levels ◽  
Negative Energy ◽  
Positive Energy ◽  
Expectation Values ◽  
Higher Derivative ◽  
Identical Manner ◽  
Heisenberg Uncertainty ◽  
The Stability

We have constructed coherent states for the higher derivative Pais–Uhlenbeck Oscillator (PUO). In the process, we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the PUO have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.

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