A Topological Classification of Interval Mappings with Finitely Many Discontinuous Points

Jinghua Liu ^[1] ; Lin Li ^[2]
1. [1] Hanshan Normal University
  
  Hanshan Normal University
  
  China
2. [2] Jiaxing University
  
  Jiaxing University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
Idioma: inglés
Enlaces
- Texto completo
Resumen
- Topological conjugacy plays an important role in the study of dynamical systems andfunctional equations. In this paper, a topological classification for monotone functionswith finitely many discontinuous points is considered. By introducing the definitionof symbolic vector for discontinuous functions, we present necessary and sufficientconditions to determine the conjugate relations between these functions. Moreover,the explicit expressions for those conjugacies are also given. Finally, as an application,our results are applied to the study of classification of generalized Lorenz maps.