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

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

2010-02-05

arxiv.org/abs/1002.1125v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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