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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  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.
KeywordsUnstable Manifold Empty Interior Heteroclinic Connection Conley Index Morse Decomposition
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