Liviu Horia Popescu

Robustness of exponential behavior in Banach spaces

We consider a generalization of the notion of exponential dichotomy in which the exponential behaviors on

Nonautonomous Dynamics with Discrete Time and Topological Equivalence

\mathbb {R}^+

Exponential dichotomy roughness on Banach spaces

R+ and

Banach function spaces and Datko-type conditions for nonuniform exponential stability of evolution families

\mathbb {R}^-

Admissible Banach function spaces for linear dynamics with nonuniform behavior on the half-line

R- need not agree at the origin, although they still satisfy a certain compatibility condition. A nontrivial example is the change from stable to unstable behavior in a given direction, such as in a saddle-node bifurcation. Our main aim is to show that this exponential behavior is robust, in the sense that it persists under sufficiently small linear perturbations. We emphasize that we consider arbitrary evolution families in Banach spaces. This includes any differentiable evolution family obtained from a nonautonomous linear equation