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.
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© 2002 Springer Science+Business Media New York
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Hale, J.K., Magalhães, L.T., Oliva, W.M. (2002). Monotonicity. In: Dynamics in Infinite Dimensions. Applied Mathematical Sciences, vol 47. Springer, New York, NY. https://doi.org/10.1007/0-387-22896-9_10
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DOI: https://doi.org/10.1007/0-387-22896-9_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3012-5
Online ISBN: 978-0-387-22896-9
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