Isoenergetic Nondegeneracy

The condition for isoenergetic nondegeneracy for a Hamiltonian

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

is

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

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.