Smoothness of Asymptotic Phase Revisited
Flaviano Battelli, Kenneth J. Palmer · Advanced Nonlinear Studies · 2011
Abstract It is well-known that solutions on the stable manifold of a hyperbolic periodic solution of an autonomous system of ordinary differential equations have an asymptotic phase which has the same order of smoothness as the vector field. In this paper we show if the system depends on a parameter that, in general, the asymptotic phase loses one order of smoothness in the parameter.