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From open quantum systems to open quantum maps

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Figure 1. An example of a potential, V ∈ C c ∞ ( R 2 ), to which the results apply: the Hamiltonian flow is hyperbolic on the trapped set in a range of energies – see [38, Appendix c]
Figure 2. A schematic view of a Poincar´e section Σ = ⊔ j Σ j for K E inside p −1 (E)
Figure 3. This figure, taken from [34], shows the case of symmetric three disc scattering problem (left), and the associated Poincar´e section (right).
Figure 4. Schematic representation of the components F ik of the Poincar´e map between the sets D ik and A ik (horizontal/vertical ellipses)
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