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.
Smoothness of asympotic phase revisited / Battelli, Flaviano; Palmer, K. J.. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 11/2011:4(2011), pp. 837-851.
Smoothness of asympotic phase revisited
BATTELLI, Flaviano;
2011-01-01
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.File in questo prodotto:
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