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On Almost Automorphic Dynamics in Symbolic Lattices
(Georgia Institute of Technology, 2002)
We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical ...
On the Gap between Random Dynamical Systems and Continuous Skew Products
(Georgia Institute of Technology, 2002)
We review the recent notion of a nonautonomous dynamical system (NDS), which has been introduced as an abstraction of both random dynamical systems and continuous skew product flows. Our focus is on fundamental analogies ...
Pullback Attracting Inertial Manifolds for Nonautonomous Dynamical Systems
(Georgia Institute of Technology, 2001)
In this paper we present an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance ...
A Spectral Characterization of Exponential Stability for Linear Time-Invariant Systems on Time Scales
(Georgia Institute of Technology, 2001)
We prove a necessary and sufficient condition for the exponential stability of time-invariant linear systems on time scales in terms of the eigenvalues of the system matrix. In particular, this unifies the corresponding ...
Gevrey Regularity of Global Attractor for Generalized Benjamin-Bona-Mahony Equation
(Georgia Institute of Technology, 2002)
We prove the Gevrey regularity of the global attractor of the dynamical system generated by the generalized Benjamin-Bona-Mahony equation with periodic boundary conditions. This result means that elements of the attractor ...