Abstract:
In this paper, we focus on the persistence of degenerate lower-dimensional invariant
tori with a normal degenerate equilibrium point in reversible systems. Based on the Herman
method and the topological degree theory, it is proved that if the frequency mapping has
nonzero topological degree and the frequency $\omega_0$ satisfies the Diophantine condition, then
the lower-dimensional invariant torus with the frequency $\omega_0$ persists under sufficiently small
perturbations. Moreover, the above result can also be obtained when the reversible system
is Gevrey smooth. As some applications, we apply our theorem to some specific examples to
study the persistence of multiscale degenerate lower-dimensional invariant tori with prescribed
frequencies.
References