A Forbidden Web in a Quasi-Dissipative System

A simultaneous transition of the system nature from everywhere smooth and conservative to piecewise smooth and quasi-dissipative is observed in a kicked billiard when adjusting single controlling parameter. The transition induces the appearance of a special kind of fat fractal forbidden web, which grows up and cuts off more parts from the original conservative stochastic web so that the remnant transient web becomes increasingly thinner. We numerically show a power law σ∝β_v, where σ is the fractal exponent of the forbidden web, β is the control parameter, and the scaling exponent v =0.288±0.007, which describes this process.