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Effects of delays on dynamics

  • Jack K. Hale
Chapter
Part of the NATO ASI Series book series (ASIC, volume 472)

Abstract

Part one of these lectures is devoted to two fixed point theorems motivated by dynamics in delay equations: an assymptotic fixed point theorem which can be applied to determine ω-periodic solutions of an (ω-periodically forced equation and an ejective fixed point theorem which can be applied to the determination of nontrivial periodic solutions of autonomous equations. Part two is devoted to large delays, Hopf bifurcations and fixed points of maps. Part three shows that small delays can destroy stability properties in delay differential equations as well as boundary control of partial differential equatons.

Keywords

Periodic Solution Periodic Orbit Hopf Bifurcation Fixed Point Theorem Functional Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Jack K. Hale
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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