Yu. Ilyashenko and A. Negut have discovered the following dynamical phenomenon. Recall that the *statistical attractor *is the smallest closed set such that almost every orbit spends almost all its time arbitrarily close to . They say that an open set is *-invisible* if almost every orbit spends a fraction of its time less than in it.

-invisibility for very small may occur for trivial reasons: if is has a small intersection with the attractor, if the transformation (or its inverse) has very large Lipschitz constant, if it is close to a structurally unstable dynamics.

Ilyashenko with Negut have built non-trivial examples of such invisible subsets. For every integer parameter , they obtain a ball of radius set among a class of skew-products over the doubling map of the circle such that:

- the Lipschitz constant is independent of ;
- the map is structurally stable;
- the attractor covers ;
- the whole space above is -invisible

Ilyashenko and Volk have just published new examples with -invisibility.

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