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Bifurcations of noncritical but nonhyperbolic invariant tori

Liujuan Chen

Abstract

Consider the time-periodic perturbations of n-dimensional autonomous systems with nonhyperbilic but noncritical closed orbits in the phase space. The elementary bifurcations to a nonhyperbilic but noncritical invariant torus of the unperturbed systems in the extended phase space (x, t) are studied and two sets of conditions on bifurcations of the invariant tori are obtained.

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Available abstract

Key concepts: Torus, Invariant (physics), Mathematics, Phase space, Periodic orbits, Mathematical analysis, Pure mathematics, Physics