Understanding homoclinic orbits

Thread starter thrillhouse86
Start date Sep 27, 2009
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Orbits

AI Thread Summary

The trace of the Jacobian of an integrable Hamiltonian system is equal to zero on the homoclinic or separatrix orbit due to a general property of Hamiltonian systems. This characteristic arises from the symplectic structure inherent in Hamiltonian dynamics. The zero trace indicates that the system's behavior is constrained in a way that reflects its integrability. Understanding this property is crucial for analyzing the stability and dynamics of orbits in Hamiltonian systems. Overall, this highlights a fundamental aspect of the mathematical framework governing such systems.

Sep 27, 2009

thrillhouse86

Hey all,

Can someone please tell me why is the trace of the Jacobian of an integrable hamiltonian system equall to zero on the homoclinic / seperatrix orbit ?

Cheers,
Thrillhouse

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Sep 28, 2009

thrillhouse86

So for anyone who is interested this is infact a general property of Hamiltonian systems that the Trace of the Jacobian is zero.

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