Strongly topological linearization with generalized exponential dichotomy

✍ Scribed by Liangping Jiang

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 233 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.06.054

✦ Synopsis

It has been proved that if x = A(t)x has a generalized exponential dichotomy and f (t, x) satisfies certain conditions, then the nonlinear system x = A(t)x + f (t, x) is topologically equivalent to its linear system x = A(t)x. In this paper, we prove that if the condition

x, where M is some positive number and a(t) is the eigenfunction of the generalized exponential dichotomy, and therefore the corresponding solutions of x = A(t)x + f (t, x) and x = A(t)x have the same stability.