HP Labs Technical Reports

Bifurcations in the Falkner Skan

Sparrow, Colin

HPL-BRIMS-96-09

Keyword(s): Falkner-Skan, gluing bifurcation; reversible system

Abstract: The Falkner-Skan equation is a reversible three dimensional system of ODEs without fixed points. A novel sequence of bifurcations, each of which creates a large set of periodic and other interesting orbits 'from infinity', occurs for each positive integer value of a parameter. Another sequence of bifurcations destroys these orbits as the parameter increases; topological constraints allow us to understand this sequence of bifurcations in considerable detail. While outlining these results, we can also make a number of possibly illuminating remarks connecting parts of the proof, well-known numerical techniques for locating and continuing periodic orbits, and recent ideas in the control of chaos.

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