Characterization of unstable periodic orbits and classical phase-space structure of the Fermi resonant system

1992 ◽  
Vol 45 (10) ◽  
pp. 7036-7048 ◽  
Author(s):  
Alexander A. Zembekov
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Space Structure ◽  
Unstable Periodic Orbits ◽  
Resonant System ◽  
Phase Space Structure ◽  
Classical Phase Space

Study of molecular phase space structure through families of periodic orbits

1989 ◽  
Vol 135 (3) ◽  
pp. 347-356 ◽  
Author(s):  
S.C. Farantos ◽  
M. Founargiotakis ◽  
C. Polymilis
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Space Structure ◽  
Phase Space Structure ◽  
Families Of Periodic Orbits

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

2017 ◽  
Vol 27 (14) ◽  
pp. 1750225 ◽  
Author(s):  
Atanasiu Stefan Demian ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Space Structure ◽  
Two Degrees Of Freedom ◽  
Phase Space Structure ◽  
Lyapunov Orbits ◽  
Lagrangian Descriptors

The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon–Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space.

Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

2020 ◽  
Vol 501 (1) ◽  
pp. 1511-1519
Author(s):  
Junjie Luo ◽  
Weipeng Lin ◽  
Lili Yang
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Eighth Order ◽  
Time Step ◽  
Extended Phase ◽  
Energy Error ◽  
Phase Space Structure ◽  
Compact Binary ◽  
Three Body

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

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