Persistence of Multiscale Degenerate Invariant Tori for Reversible Systems with Multiscale Degenerate Equilibrium Points

    2022, Volume 27, Number 6, pp.  733-756

    Author(s): Zhang D., Qu R.

    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.
    Keywords: Reversible systems, KAM iteration, topological degree, degenerate lower-dimensional tori, degenerate equilibrium points
    Citation: Zhang D., Qu R., Persistence of Multiscale Degenerate Invariant Tori for Reversible Systems with Multiscale Degenerate Equilibrium Points, Regular and Chaotic Dynamics, 2022, Volume 27, Number 6, pp. 733-756



    Access to the full text on the Springer website