A Note on Stronger Forms of Sensitivity for Non-Autonomous Dynamical Systems on Uniform Spaces.
Entropy (Basel)
; 26(1)2024 Jan 02.
Article
en En
| MEDLINE
| ID: mdl-38248173
ABSTRACT
This paper introduces the notion of multi-sensitivity with respect to a vector within the context of non-autonomous dynamical systems on uniform spaces and provides insightful results regarding N-sensitivity and strongly multi-sensitivity, along with their behaviors under various conditions. The main results established are as follows (1) For a k-periodic nonautonomous dynamical system on a Hausdorff uniform space (S,U), the system (S,fk∘â¯∘f1) exhibits N-sensitivity (or strongly multi-sensitivity) if and only if the system (S,f1,∞) displays N-sensitivity (or strongly multi-sensitivity). (2) Consider a finitely generated family of surjective maps on uniform space (S,U). If the system (S,f1,∞) is N-sensitive, then the system (S,fk,∞) is also N-sensitive. When the family f1,∞ is feebly open, the converse statement holds true as well. (3) Within a finitely generated family on uniform space (S,U), N-sensitivity (and strongly multi-sensitivity) persists under iteration. (4) We present a sufficient condition under which an nonautonomous dynamical system on infinite Hausdorff uniform space demonstrates N-sensitivity.
Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Diagnostic_studies
Idioma:
En
Revista:
Entropy (Basel)
Año:
2024
Tipo del documento:
Article
País de afiliación:
China