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Mathematics - Dynamical Systems & Differential Equations | Stability of Nonautonomous Differential Equations

Stability of Nonautonomous Differential Equations

Series: Lecture Notes in Mathematics, Vol. 1926

Barreira, Luis, Valls, Claudia

2008, XIV, 291 p.

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Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

Content Level » Research

Keywords » Lyapunov stability - Stability theory - center manifolds - invariant manifolds - nonuniform hyperbolicity - topological conjugacies

Related subjects » Dynamical Systems & Differential Equations

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