2021/09/13 by Sebastián Herrero, Herrero, Sebastián, Nelda Jaque +1
Engineering · #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2109.06003
openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study two notions of expansiveness for continuous semiflows: expansiveness in the sense of Alves, Carvalho and Siqueira (2017), and an adaptation of positive expansiveness in the sense of Artigue (2014). We prove that if X is a metric space and ϕ is an expansive semiflow on X according to the first definition, then the semiflow ϕ is trivial and the space X is uniformly discrete. In particular, if X is compact then it is finite. With respect to the second definition, we prove that if X is a compact metric space and ϕ is a positive expansive semiflow on it, then X is a union of at most finitely many closed orbits, unbranched tails and isolated singularities.