Chaotic dynamical systems associated with tilings of $\R^N$

TL;DR

This paper studies chaotic dynamical systems on spaces formed by regular tilings of Euclidean space, proving their chaos properties and introducing a synchronization method for secure communication.

Contribution

It establishes chaos in dynamical systems on tilings of $ ^N$ and proposes a chaos-based synchronization technique for information masking.

Findings

Systems are chaotic in the sense of Devaney.

Existence of at least one positive Lyapunov exponent.

Introduces a chaos synchronization mechanism for secure communication.

Abstract

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus $\T ^N$. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.