scholarly journals Symbolic dynamics: from the N-centre to the (N + 1)-body problem, a preliminary study

2013 ◽  
Vol 21 (3) ◽  
pp. 371-413 ◽  
Author(s):  
Nicola Soave
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Preliminary Study

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.

Symbolic dynamics in the symmetric collinear four-body problem

2004 ◽  
Vol 5 (1) ◽  
pp. 75-100 ◽  
Author(s):  
Ernesto A. Lacomba ◽  
Mario Medina
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Four Body Problem

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 Symbolic dynamics in the restricted elliptic isosceles three body problem

2021 ◽  
Vol 294 ◽  
pp. 143-177
Author(s):  
Marcel Guardia ◽  
Jaime Paradela ◽  
Tere M. Seara ◽  
Claudio Vidal
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Symbolic dynamics of the elliptic rectilinear restricted 3--body problem

2008 ◽  
Vol 1 (4) ◽  
pp. 541-555 ◽  
Author(s):  
Samuel R. Kaplan ◽  
◽  
Ernesto A. Lacomba ◽  
Jaume Llibre ◽  
◽  
...  
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem
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