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Analytical tools to study the criticality at the outer boundary of potential centers

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Figure 2.1: Embedding of R2 into RP2.
Figure 2.2: Interpretation of the periodic orbit γh.
Figure 2.3:Graph of V for admissible potential systems with finite
Figure 3.1: Conjectural bifurcation diagram for the period function ofthe differential system (3.1), where the doted and bold curves consist oflocal bifurcation values at the inner and outer boundary, respectively.The parameters in the grey region correspond to systems with exactlyone critical periodic orbit, whereas parameters in the white region cor-respond to systems with monotonic period function.
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