Absolutely continuous invariant measures that cannot be observed experimentally. (English) Zbl 1090.37041

Summary: We study an example of a random map where the component maps have absolutely continuous invariant measures (acims), but where computer experiments reveal the surprising fact that all orbits eventually fall into a stable periodic orbit. This is all the more surprising as we prove that this random map admits an acim \(\mu\). We study this phenomenon and explain why \(\mu\) cannot be observed experimentally.


37H99 Random dynamical systems
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37C27 Periodic orbits of vector fields and flows
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