| Tunnelling in the presence of real horseshoe chaos is discussed as an ideal situation describing chaotic tunneling. In the case, the tunnelling set coincides exactly with the forward Julia set. Role of the forward and backward Julia set, which are the stable-unstable manifolds of chaotic invariant set, in the formation of tunnelling paths is demonstrated in the idealized situation. The tunnelling paths first travel along the forward Julia set, go close to the chaotic invariant set, and finally land along the intersection of the forward Julia set with the real phase space. |
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