Sentence examples similar to degeneracy condition from inspiring English sources

Also, the degeneracy conditions of the non-hyperbolic point were derived and the dynamics of the resulting system on the center manifold near the double-zero degenerate point by using center manifold and normal form methods were examined.

Rüssmann's non-degeneracy condition.

However, the non-degeneracy condition is used in Theorem 1.2.

So the non-degeneracy condition in symplectic mappings and that in Hamiltonian systems are different.

However, by using the Ljusternik-Schnirelmann category no non-degeneracy condition is required.

All the bifurcations that we have identified in the model, both analytically and numerically, satisfied the non-degeneracy condition.

Xu and You [24] obtained a similar result under the Rüssmann non-degeneracy condition by an improved KAM method.

The second one is the non-degeneracy condition, which will result in a more complicated proof for estimate of measure.

For any injective map (g:[n] rightarrow [n']) in (Delta ), the transition functor (g^*) of the Grothendieck fibration (Delta ^L_M I rightarrow Delta ) preserves the non-degeneracy condition.

We construct here a family of mixed type solutions (u1,ε,u2,ε), ε>0 for an arbitrary configuration of vortex points under a mild non-degeneracy condition.

Popov [23] obtained the Gevrey-smoothness, a notion intermediate between (C^{infty} -smoothness and analyticity, of invariant tori in the frequencies under the Kolmogorov non-degeneracy condition.