Optimal regularity of robustness for parameterized perturbations

✍ Scribed by Luis Barreira; Claudia Valls

• Publisher: Elsevier Science
• Year: 2010
• Tongue: French
• Weight: 144 KB
• Volume: 134
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/j.bulsci.2009.12.003

✦ Synopsis

For exponential dichotomies defined by nonautonomous linear equations, we show that sufficiently small C 1 -parameterized perturbations originate a family of exponential dichotomies of class C 1 in the parameter. We consider the general case of nonuniform exponential dichotomies, and also the general case of arbitrary growth rates of the form e λρ (t) where ρ is an arbitrary function. This includes the usual exponential behavior as a very special case when ρ(t) = t.