2025/06/12 by Hongbo Zeng, Zeng, Hongbo
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Fixed Point Theorems Analysis #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2506.10455
openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a nondegenerate compact perfect and Hausdorff topological space X,n∈ ℕ and a function f:X→ X, we consider the n-fold symmetric product of X, Fn(X) and the induced function Fn(f):Fn(X)→ Fn(X). If n≥2, we consider the n-fold symmetric product suspension of X, SFn(X) and the induced functionSFn(f):SFn(X)→ SFn(X). In this paper, we study the relationships between the following statements: (1) f∈ M,(2) Fn(f)∈ M, and (3)SFn(f)∈ M, where M is one of the following classes of map: sensitive, cofinitely sensitive, multi-sensitive, Z-transitive, quasi-periodic, accessible, indecomposable, multi-transitive, \bigtriangleup-transitive, \bigtriangleup-mixing, Martelli's chaos, Transitive, F-system, TT++, Touhey, two-sided transitive, fully exact, strongly transitive. These results improve and extend some existing ones.