Figures - overview - Chapter 5

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(image on first page of Chapt. 5)
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Figure 5.1: An illustration of the Poincaré map definition.
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Figure 5.2: (a) An example of a traditional Poincaré map visualization [76].  (b) An example of a 3D Poincaré map [15].
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Figure 5.3: Poincaré map visualization by Abraham and Shaw [1].
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Figure 5.4: Visualizing a non-linear saddle cycle.
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Figure 5.5: Visualizing an cycle attractor using spot noise.
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Figure 5.6: Visualizing a non-hyperbolic saddle cycle.
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Figure 5.7: Visualizing why pq is sometimes more expressive than  p.
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Figure 5.8: Visualizing  (a)  $\{(\mathbf{x}_i,\mathbf{p}(\mathbf{x}_i))\}$ vs.  (b)  $\{(\mathbf{x}_i,\mathbf{p}^3(\mathbf{x}_i))\}$.
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Figure 5.9: Evaluating the initial texture after two applications of  w.
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Figure 5.10: Images resulting from one, two, and eleven applications of warp function  w, i.e., $\mathbf{w}(\mathcal{S})$, $\mathbf{w}^2(\mathcal{S})$, and  $\mathbf{w}^{11}(\mathcal{S})$.
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Figure 5.11: Visualizing flow properties not encoded within the Poincaré map.
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Figure 5.12: Visualizing supplementary information in 3D. [left image] [right image]
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Figure 5.13: Extreme phase relations as difficult cases for the visualization of Poincaré maps. [left image] [right image]
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Figure 5.14: Combined visualization techniques to disambiguate results. [left image] [right image]