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We consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.

We present simple examples of (competitive) two species systems with complicated dynamic behaviour. From almost all initial conditions one of the two species dies out. But the survivor is unpredictable: The basins of the two chaotic one-species attractors are everywhere dense and intermingled.

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