**Short description:**

The Rössler map is a diffeomorphism of the plane given by
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R(x,y)=(R*_{1}(x,y),R_{2}(x,y)),
R_{1}(x,y)=3.8x(1-x)-0.1y,
R_{2}(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 following
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Lemma.
Define W=[0.01,0.99]´[-0.33,0.27]. The set R(W) is a subset of the set W.
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Since *W* is a compact set the previous Lemma implies the existence of a **compact, connected, invariant set** - an attracting set.

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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.
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Applet settings:

**clear** button - clears the Graphics Frame,

**default values** button - sets the drawing region on *[0,1]´[-0.5,0.5]* and clears the Graphics Frame.

**Wimage** button - shows the iterations of the boundary of W, i.e. R^{n}(W).

**show trajectory** button - shows the trajectory of a point. You can choose a start point from the set *W* and the number of iterations.

These operations are usually long-lasting, so the title of the Graphics Frame is changed on **wait**.

**Zoom in:** In the Graphics Frame you can select some subset of the drawing region.
Then click **clear** and **show trajectory** buttons.