Chaotic dynamical systems associated with tilings of ${R}^{N}$

Lionel Rosier (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Domaines: Equations aux dérivées partielles [math.AP]

Lionel Rosier. Chaotic dynamical systems associated with tilings of ${R}^{N}$. Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption, IGI Global, pp.19-41, 2010, ⟨10.4018/978-1-61520-737-4.ch002⟩. ⟨hal-00453068⟩