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On the geometric formulation of Hamiltonian dynamics
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10.1063/1.4791588
/content/aip/journal/chaos/23/1/10.1063/1.4791588
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4791588
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The Henon-Heiles System: Left column corresponds to and right column corresponds to . The upper row corresponds to the Poincare sections method, where the bottom row corresponds to the geometric method maps (for the geometric maps we actually fixed , to make the white spots within the initial connectedness component more distinguishable). The value is exactly the predicted threshold energy, at which we see the white regions from the outer components cross into the previously bounded component.

Image of FIG. 2.
FIG. 2.

The He atom system: Left column corresponds to and right column corresponds to . The upper row corresponds to the Poincare sections method, where the bottom row corresponds to the geometric method maps. The predicted threshold energy is just below –2.55, in agreement with Ref. 26 .

Image of FIG. 3.
FIG. 3.

The diamagnetic Kepler System: Left column corresponds to and right column corresponds to . Upper row corresponds to the Poincare sections method, where the bottom row corresponds to the geometric method maps. The predicted threshold energy is just below –0.093.

Image of FIG. 4.
FIG. 4.

The geometric method map for the Hamiltonian system ; energy was fixed to .

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/content/aip/journal/chaos/23/1/10.1063/1.4791588
2013-02-15
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the geometric formulation of Hamiltonian dynamics
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4791588
10.1063/1.4791588
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