Homoclinic orbits of the Kovalevskaya top with perturbations

2005 ◽  
Vol 85 (4) ◽  
pp. 277-302 ◽  
Author(s):  
J.L. Kuang ◽  
A.Y.T. Leung
Keyword(s):  
Homoclinic Orbits ◽  
Kovalevskaya Top

scholarly journals A Melnikov Method for Homoclinic Orbits with Many Pulses

1998 ◽  
Vol 143 (2) ◽  
pp. 105-193 ◽  
Author(s):  
Roberto Camassa ◽  
Gregor Kovačič ◽  
Siu-Kei Tin
Keyword(s):  
Melnikov Method ◽  
Homoclinic Orbits

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

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.

scholarly journals Homoclinic orbits and Lie rotated vector fields

2000 ◽  
Vol 24 (3) ◽  
pp. 187-192
Author(s):  
Jie Wang ◽  
Chen Chen
Keyword(s):  
Limit Cycles ◽  
Homoclinic Orbit ◽  
Vector Fields ◽  
Homoclinic Orbits ◽  
Singular Points ◽  
Definition Of

Based on the definition of Lie rotated vector fields in the plane, this paper gives the property of homoclinic orbit as parameter is changed and the singular points are fixed on Lie rotated vector fields. It gives the conditions of yielding limit cycles as well.

scholarly journals Erratum to: Homoclinic orbits for an unbounded superquadratic Hamiltonian systems

2010 ◽  
Vol 18 (1) ◽  
pp. 115-115
Author(s):  
Jun Wang ◽  
Junxiang Xu ◽  
Fubao Zhang ◽  
Lei Wang
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits

scholarly journals Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

2006 ◽  
Vol 214 (2) ◽  
pp. 169-181 ◽  
Author(s):  
Kazuyuki Yagasaki ◽  
Thomas Wagenknecht
Keyword(s):  
Homoclinic Orbits ◽  
Reversible Systems
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