Monotone Dynamical Systems with Polyhedral Order Cones and Dense\n Periodic Points

2016/11/28 by Morris W. Hirsch, Hirsch, Morris W.
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1611.09251

openalex publication_date 2016/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a subset of Rⁿ whose interior is connected and dense in X, ordered\nby a polyhedral cone in Rⁿ with nonempty interior. Let T be a monotone\nhomeomorphism of X whose periodic points are dense. Then T is periodic.\n

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• Monotone local flows with dense periodic orbits
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• Monotonicity and Contraction on Polyhedral Cones