Monotone Dynamical Systems

1 Strongly Order-Preserving Semiflows 6 1.1 Definitions and Basic Results . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Nonordering of Omega Limit Sets . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Local Semiflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 The Limit Set Dichotomy . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Q is plentiful . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Stability in Normally Ordered Spaces . . . . . . . . . . . . . . . . . . . . 21 1.7 Stable Equilibria in Strongly Ordered Banach Spaces . . . . . . . . . . . 24 1.8 The Search for Stable Equilibria . . . . . . . . . . . . . . . . . . . . . . . 27

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