scholarly journals Uniqueness of connecting orbits in the equation Y(3) = Y2 − 1

1986 ◽  
Vol 114 (2) ◽  
pp. 584-592 ◽  
Author(s):  
Christopher K McCord
Keyword(s):  
Connecting Orbits

HETEROCLINIC ORBITS FOR MONOTONE TWIST MAPS THROUGH A VARIATIONAL PRINCIPLE

2001 ◽  
Vol 11 (09) ◽  
pp. 2451-2461
Author(s):  
TIFEI QIAN
Keyword(s):  
Variational Principle ◽  
Variational Method ◽  
Fixed Points ◽  
Heteroclinic Orbit ◽  
Geometric Method ◽  
Heteroclinic Orbits ◽  
Constructive Approach ◽  
Connecting Orbits ◽  
Relative Ease ◽  
Twist Maps

The variational method has shown many advantages over the geometric method in proving the existence of connecting orbits since it requires much weaker hyperbolicity and less smoothness. Many results known to be difficult to obtain by the geometric method can now be obtained by a variational principle with relative ease. In particular, a variational principle provides a constructive approach to the existence of heteroclinic orbits. In this paper a variational principle is used to construct a heteroclinic orbit between an adjacent minimal pair of fixed points for monotone twist maps on (ℝ/ℤ) × ℝ. Application of our results to a standard map is also given.

scholarly journals Connecting orbits and invariant manifolds in the spatial restricted three-body problem

Nonlinearity ◽  
2004 ◽  
Vol 17 (5) ◽  
pp. 1571-1606 ◽  
Author(s):  
G Gómez ◽  
W S Koon ◽  
M W Lo ◽  
J E Marsden ◽  
J Masdemont ◽  
...  
Keyword(s):  
Body Problem ◽  
Invariant Manifolds ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Connecting Orbits ◽  
Three Body

On the Existence of Connecting Orbits

1996 ◽  
Vol 15 (4) ◽  
pp. 779-787
Author(s):  
Yu Shu-Xiang
Keyword(s):  
Connecting Orbits
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