We report a crisis that is induced by an escape from a fat strange set formed by the forward images of an oscillating discontinuity borderline. It is analytically and numerically shown that the iteration lifetime obeys the universal power-law dependence on the controlling parameter and the scaling exponent takes an exceptional large value, i.e.v=1.72 ± 0.04. The strange repeller, which appears after the crisis, is also a fat fractal. To our knowledge, this is the first example for a new mechanism that produces supertransients.
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