Nonstandard analysis of asymptotic points and exponential decay of expansivity constants
Volume 271 / 2025
Fundamenta Mathematicae 271 (2025), 237-254
MSC: Primary 37B05; Secondary 03H05
DOI: 10.4064/fm241014-2-7
Published online: 3 November 2025
Abstract
We apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit doubly-asymptotic points in terms of the decay of expansivity constants of the powers of the system.
