Work

The Shadowing Property for Piecewise Monotone Interval Maps

Year: 2026

Type: article

Abstract: The property of shadowing is fundamental in both the theory of symbolic dynamics as well as continuous dynamical systems. A quintessential class of discontinuous dynamical systems are those driven by transitive piecewise monotone interval maps and in particular β-transformations, namely transformations of the form Tβ,α:x↦βx+α (mod 1) acting on [0, 1]. We provide a short elegant proof showing that this class of dynamical systems do not possess the property of shadowing, complementing and extending the work of Liang Chen and Raquel Portela.

Source: American Mathematical Monthly

DOI: 10.1080/00029890.2026.2686074

Authors: A. Bura, C. Good, T. Samuel

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Engineering and Physical Sciences Research Council

Awards: G1084194831, EPSRC Centre for Doctoral Training in Topological Design, Complexity of random substitution tilings

OpenAlex ID: W4407310278

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