Chaos on Peano continua
Abstract
Generalizing the result of Agronsky and Ceder (1991), we prove that every Peano continuum admits a continuous transformation that is exact Devaney chaotic; that is, it has a dense set of periodic points, and every nonempty open set covers the entire space in finitely many iterations. We identify a natural class of Peano continua, containing all one-dimensional continua and all connected absolute neighborhood retracts, which allows us to create locally small perturbations. Using this method, we prove that within these specific classes of continua, exact Devaney chaotic systems are dense in all chain transitive systems, mixing systems are generic among chain transitive systems and shadowing is generic among all continuous systems.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Chaos control and synchronization
Cellular Automata and Applications
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 55
- Issue
- 0
- Pages
- 132–149
- Publication date
- 1 January 2026
- Language
- EN