Linear Skew Product Flows Exponential Dichotomies And Structural Stability
Date of Award
Doctor of Arts (D.A.)
This thesis is primarily concerned with linear, time-varying ordinary differential equations. The problem is treated in the context of linear skew product flows and its generalization to fiber-preserving flows and diffeomorphisms. A criterion of Coppel is generalized to get sufficient conditions obtained by Sacker and Sell for the existence of an exponential dichotomy for a class of equations, which includes those with almost periodic coefficients. The results obtained are also used to study the dual linear skew product flow and then applied to structural stability to obtain Bronstein's result that if a diffeomorphism satisfies the transversality condition then it is Axiom A.
Elkhoury, Walid Nicholas, "Linear Skew Product Flows Exponential Dichotomies And Structural Stability" (1984). Dissertations from ProQuest. 1425.