Quantum level structures at a Fermi resonance with angular momentum: classical periodic orbits, catastrophe maps and quantum monodromy

2005 ◽  
Vol 7 (14) ◽  
pp. 2731 ◽  
Author(s):  
C. D. Cooper ◽  
M. S. Child
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Fermi Resonance ◽  
Quantum Level

Bound orbits around modified Hayward black holes

2021 ◽  
Author(s):  
Bo Gao ◽  
Xue-Mei Deng
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Periodic Orbits ◽  
Kerr Black Hole ◽  
Periodic Oscillations ◽  
Test Particles ◽  
Spin Parameter ◽  
Bound Orbits

The neutral time-like particle’s bound orbits around modified Hayward black holes have been investigated. We find that both in the marginally bound orbits (MBO) and the innermost stable circular orbits (ISCO), the test particle’s radius and its angular momentum are all more sensitive to one of the parameters [Formula: see text]. Especially, modified Hayward black holes with [Formula: see text] could mimic the same ISCO radius around the Kerr black hole with the spin parameter up to [Formula: see text]. Small [Formula: see text] could mimic the ISCO of small-spinning test particles around Schwarzschild black holes. Meanwhile, rational (periodic) orbits around modified Hayward black holes have also been studied. The epicyclic frequencies of the quasi-circular motion around modified Hayward black holes are calculated and discussed with respect to the observed Quasi-periodic oscillations (QPOs) frequencies. Our results show that rational orbits around modified Hayward black holes have different values of the energy from the ones of Schwarzschild black holes. The epicyclic frequencies in modified Hayward black holes have different frequencies from Schwarzschild and Kerr ones. These might provide hints for distinguishing modified Hayward black holes from Schwarzschild and Kerr ones by using the dynamics of time-like particles around the strong gravitational field.

Periodic Orbits of Radially Symmetric Systems with a Singularity: the Repulsive Case

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Periodic Forcing ◽  
The Third ◽  
Large Angular Momentum ◽  
Symmetric Systems

AbstractWe study radially symmetric systems with a singularity of repulsive type. In the presence of a radially symmetric periodic forcing, we show the existence of three distinct families of subharmonic solutions: One oscillates radially, one rotates around the origin with small angular momentum, and the third one with both large angular momentum and large amplitude. The proofs are carried out by the use of topological degree theory.

scholarly journals Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Shengjun Li ◽  
Yuming Zhu
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
The Other ◽  
Topological Degree Theory ◽  
Families Of Periodic Orbits ◽  
Large Angular Momentum

We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude.

The Hénon and Heiles Problem in Three Dimensions.

1998 ◽  
Vol 08 (06) ◽  
pp. 1199-1213 ◽  
Author(s):  
S. Ferrer ◽  
M. Lara ◽  
J. Palacián ◽  
J. F. San Juan ◽  
A. Viartola ◽  
...  
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Relative Equilibria ◽  
Three Dimensions ◽  
The Third ◽  
Numerical Studies ◽  
Families Of Periodic Orbits ◽  
Poincaré Surfaces Of Section

This paper is the first part of a study of the Hénon and Heiles problem in three dimensions. Due to the axial symmetry of the Hamiltonian, the third component of the angular momentum is an integral and the system is considered as a Hamiltonian with two degrees of freedom. As functions of that integral, we show the existence of three circular trajectories around the axis Oz and a domain for which we have bounded motions. In the part of that domain near the origin, the corresponding dynamical system is treated as a perturbed harmonic oscillator in 1–1–1 resonance. We present some numerical studies searching for periodic orbits, showing the corresponding Poincaré surfaces of section. In addition, we obtain some natural families of periodic orbits associated with the relative equilibria of the fourth order normalized system.

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