Fixed points on null and tame flows for groups of automorphisms

2025/07/16 by Alessandro Codenotti, Codenotti, Alessandro
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2507.12239

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Using a generalization of the Kechris-Pestov-Todorčević correspondence due to Nguyen Van Thé we obtain fixed point theorems for null and tame actions of groups of the form Aut(\mathcal F), where F is a Fraïssé structure. In particular we show that if Age(\mathcal F) is a free joint embedding class, then every null flow Aut(\mathcal F)\curvearrowright X has a fixed point, while if Age(\mathcal F) is a free amalgamation class, then every tame flow Aut(\mathcal F)\curvearrowright X has a fixed point.

Citations

• Coherent extension of partial automorphisms, free amalgamation, and\n automorphism groups
• Fixed points in compactifications and combinatorial counterparts
• Fraïssé Structures with Universal Automorphism Groups
• Katetov functors
• The dynamical hierarchy for Roelcke precompact Polish groups
• Independence in topological and C*-dynamics
• Hereditarily non-sensitive dynamical systems and linear representations

Related

• A note on fixed point free automorphisms of groups related to finite fields
• A Fixed Point Theorem for Deformation Spaces of G-trees
• The rhombic dodecahedron and semisimple actions of Aut(F_n) on CAT(0) spaces
• Fixating Group Actions
• Fixed points of endomorphisms of virtually free groups