Center manifolds for impulsive equations under nonuniform hyperbolicity

✍ Scribed by Luis Barreira; Claudia Valls

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 259 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.10.032

✦ Synopsis

We establish the existence of smooth center manifolds under sufficiently small perturbations of an impulsive linear equation. In particular, we obtain the C 1 smoothness of the manifolds outside the jumping times. We emphasize that we consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential trichotomy.