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Monotonicity

  • Jack K. Hale
  • Luis T. Magalhães
  • Waldyr M. Oliva
Chapter
  • 476 Downloads
Part of the Applied Mathematical Sciences book series (AMS, volume 47)

Abstract

In the last years several papers have appeared which deal with global properties of monotone dynamical systems, that is, maps or semiflows admitting a discrete Lyapunov functional. We refer also to the book [192] for some aspects of the theory as well as extensive references. Our objective in this chapter is to concentrate on certain properties of monotonicity. Between these properties we mention: transversality, Morse—Smale structure, connections between critical elements, Morse decomposition, etc. All of them are used to clarify the structure of the flow including the determination of stability under perturbation of parameters.

Keywords

Unstable Manifold Empty Interior Heteroclinic Connection Conley Index Morse Decomposition 
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 New York 2002

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Luis T. Magalhães
    • 2
  • Waldyr M. Oliva
    • 2
  1. 1.School of MathematicsGeorgia TechAtlantaUSA
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal

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