Conjecture 1.1: Let \( \mathbb{T}^{2} \) be a closed two-dimensional box with periodic boundary conditions. Consider \( \Omega \subsetneq \mathbb{T}^{2} \) a closed domain occupied by a two-dimensional radioactive source and \( \mathcal{C} \) a two-dimensional cat embedded in \( \mathbb{T}^{2} \setminus \Omega \) .
Apply, now, Arnol'ds cat map \( \Gamma \) to \( \mathbb{T}^{2} \setminus \Omega \rightarrow \mathbb{T}^{2} \). Then, the probability that the cat dies goes very rapidly to \( 1\).
We have a beautiful proof of the above statement, but this internet is too small for the proof to fit in.
Apply, now, Arnol'ds cat map \( \Gamma \) to \( \mathbb{T}^{2} \setminus \Omega \rightarrow \mathbb{T}^{2} \). Then, the probability that the cat dies goes very rapidly to \( 1\).
We have a beautiful proof of the above statement, but this internet is too small for the proof to fit in.
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