Abstract
Certain orbits of area preserving maps of the plane appear to wander randomly and to densely fill regions of the plane having positive Lebesgue measure. These regions are called ergodic zones. Trellises (or homoclinic tangles) embedded within these zones are shown to guide the transport of ensembles of points. Trellises or tangles can be localized within what are called resonance zones. Transport through resonance zones is calculated using the MacKay-Meiss-Percival action principle.
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