R(x,y)=(R1(x,y),R2(x,y)), R1(x,y)=3.8x(1-x)-0.1y, R2(x,y)=0.2(y-1.2)(1-1.9x).
Numerical simulation of the discrete dynamical system induced by the Rössler map shows the existence of an attracting set with very complicated and chaotic dynamics. It is easy to prove the followingLemma. Define W=[0.01,0.99]´[-0.33,0.27]. The set R(W) is a subset of the set W.
Since W is a compact set the previous Lemma implies the existence of a compact, connected, invariant set - an attracting set.Theorem. The six iteration of the Rössler map is semicojugated to the full shift on two symbols. Moreover, the preimage of an arbitrary periodic sequence of symbols contains a periodic point with the same basic period.