---
abstract: 'We offer an overview of the specification property, its relatives and their consequences. We examine relations between specification-like properties and such notions as: mixing, entropy, the structure of the simplex of invariant measures, and various types of the shadowing property. We pay special attention to these connections in the context of symbolic dynamics.'
address:
- ' Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Łojasiewicza 6, 30-348 Kraków, Poland'
- ' Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Łojasiewicza 6, 30-348 Kraków, Poland'
- 'AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland'
author:
- Dominik Kwietniak
- 'Martha [Ł]{}cka'
- Piotr Oprocha
bibliography:
- 'bibliography.bib'
title: 'A panorama of specification-like properties and their consequences'
---

The specification property is the ability to find a single point following ${\varepsilon}$-close an arbitrary collection of orbit segments, provided that the tracing point is allowed to spend a fixed (dependent on ${\varepsilon}$) time between consecutive segments.

Rufus Bowen introduced the specification property in his seminal paper of 1971 on Axiom A diffeomorphisms [@Bowen71]. In recent years this notion and its generalizations served as a basis for many 