EAN: 9783319901091

SPRINGERBRIEFS IN MATHEMATICS ADMISSIBILITY A...

This book gives a comprehensive overview of the relationship between admissibility and
hyperbolicity. Essential theories and selected developments are discussed with highlights to
applications. The dedicated readership includes researchers and graduate students specializing
in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to
have a broad view of the topic and working knowledge of its techniques. The book may also be
used as a basis for appropriate graduate courses on hyperbolicity  the pointers and references
given to further research will be particularly useful.The material is divided into three parts:
the core of the theory  recent developments  and applications. The first part pragmatically
covers the relation between admissibility and hyperbolicity  starting with the simpler case of
exponential contractions. It also considers exponential dichotomies  both for discrete and
continuous time  and establishes corresponding results building on the arguments for
exponential contractions. The second part considers various extensions of the former results 
including a general approach to the construction of admissible spaces and the study of
nonuniform exponential behavior. Applications of the theory to the robustness of an exponential
dichotomy  the characterization of hyperbolic sets in terms of admissibility  the relation
between shadowing and structural stability  and the characterization of hyperbolicity in terms
of Lyapunov sequences are given in the final part.

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