  We study the effect of homogeneous noise on the escape rate of strongly
chaotic area-preserving maps with a small opening. While in the noiseless
dynamics the escape rate analytically depends on the instability of the
shortest periodic orbit inside the hole, adding noise overall enhances escape,
which, however, exhibits a non-trivial response to the noise amplitude,
featuring an initial plateau and a successive rapid growth up to a saturation
value. Numerical analysis is performed on cat maps with a hole, and the salient
traits of the response to noise of the escape rate are reproduced analytically
by an approximate model.

Chaotic Dynamics