scholarly journals Symbolic Dynamics, Mixing and Entropy in the Three-Body Problem

2016 ◽  
Vol 25 (3) ◽  
Author(s):  
A. Mylläri ◽  
V. Orlov ◽  
A. Chernin ◽  
A. Martynova ◽  
T. Mylläri
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Initial Conditions ◽  
Free Fall ◽  
Equal Mass ◽  
Binary Collision ◽  
Three Body Problem ◽  
Symbolic Sequences ◽  
Three Body ◽  
Sensitivity To Initial Conditions

AbstractWe use symbolic dynamics in the classic equal-mass free-fall three-body problem. Different methods for constructing symbolic sequences (in the process of numerical integration of trajectories) allow one to demonstrate (and illustrate on the Agekian-Anosova map) sensitivity to initial conditions, estimate entropies (Shannon, Markov and others), plot binary collision curves, reveal systems with intensive triple interactions (interplay), etc.

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

Periodic orbits in the free-fall three-body problem

2016 ◽  
Vol 60 (12) ◽  
pp. 1083-1089 ◽  
Author(s):  
V. V. Orlov ◽  
V. A. Titov ◽  
L. A. Shombina
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Free Fall ◽  
Three Body Problem ◽  
Three Body

Triple approaches in the plane isosceles equal-mass three-body problem

2001 ◽  
Vol 27 (10) ◽  
pp. 678-682
Author(s):  
V. V. Orlov ◽  
A. V. Petrova ◽  
A. I. Martynova
Keyword(s):  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals Saari’s homographic conjecture for a planar equal-mass three-body problem under the Newton gravity

2012 ◽  
Vol 45 (34) ◽  
pp. 345202 ◽  
Author(s):  
Toshiaki Fujiwara ◽  
Hiroshi Fukuda ◽  
Hiroshi Ozaki ◽  
Tetsuya Taniguchi
Keyword(s):  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals New periodic orbits in the planar equal-mass three-body problem

2018 ◽  
Vol 38 (4) ◽  
pp. 2187-2206
Author(s):  
Rongchang Liu ◽  
◽  
Jiangyuan Li ◽  
Duokui Yan
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals Saari’s homographic conjecture for a planar equal-mass three-body problem under a strong force potential

2012 ◽  
Vol 45 (4) ◽  
pp. 045208 ◽  
Author(s):  
Toshiaki Fujiwara ◽  
Hiroshi Fukuda ◽  
Hiroshi Ozaki ◽  
Tetsuya Taniguchi
Keyword(s):  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Strong Force ◽  
Three Body ◽  
Force Potential
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