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Isoenergetic Nondegeneracy

The condition for isoenergetic nondegeneracy for a Hamiltonian

\begin{displaymath}
H=H_0({\bf I})+\epsilon H_1({\bf I}, \boldsymbol{\theta})
\end{displaymath}

is

\begin{displaymath}
\left\vert\matrix{
{\partial^2H_0\over\partial I_i\partial ...
...\cr
{\partial H_0\over\partial I_j} & 0\cr}\right\vert\not=0,
\end{displaymath}

which guarantees the Existence on every energy level surface of a set of invariant tori whose complement has a small Measure.


References

Tabor, M. Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, pp. 113-114, 1989.




© 1996-9 Eric W. Weisstein
1999-05-26