A dispersive dynamical system that is chain transitive

Abstract

This paper compares the notions of Auslander generalized recurrence and chain recurrence of dynamical systems. Generalized recurrent points are chain recurrent, however, chain recurrent points may not be generalized recurrent of any order. Because of the absence of recursiveness, the dispersive systems have no generalized recurrent point. Examples of systems with generalized recurrent points and systems with no generalized recurrent points are presented. The main example shows a dispersive system that is chain transitive.

Keywords

• Dynamical system
• Higher prolongation
• Generalized recurrence
• Chain recurrence
• Dispersiveness