| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 287
Z. Zheng and D.Roose
The Behaviour of the Floquet Multipliers of Periodic Solutions Near a Homoclinic Orbit
Abstract
In this paper, we describe the behaviour of the moduli of the Floquet multipliers of periodic solutions near a homoclinic orbit. We discuss the relation between the Floquet multipliers and the eigenvalues of the equilibrium point at which the homoclinic orbit emanates. For two-dimensional problems, for which the equilibrium point has two real eigenvalues, we derive an asymptotic estimate for the nontrivial Floquet mulitpliers in terms of the period. For more complicated situations (higher dimensional problems, complex conjugate pairs of eigenvalues), we perform numerical experiments for some model equations, showing that eigenvalues with large negative real part cause small Floquet multipliers.
report.pdf / mailto: D. Roose