2021/01/02 by Luis Ferrari, Ferrari, Luis
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2101.00498
openalex publication_date 2021/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,d) be a metric space and f: X → X be a homeomorphism. We say that a dynamical system (X,f) is expansive, with constant of expansivity c ∈ \mathbbR+, if for all x,y ∈ X , x ≠ y, exists n ∈ ℤ, such that d(fn(x), fn(y)) >c. In this paper we will use the theory of Nonstandard Analysis to study a subfamily of these dynamics, which verify that for all x,y ∈ X, if x≠ y then the set \lbrace n ∈ ℤ : d(fn(x), fn(y) > c \rbrace is infinite.