HP Labs Technical Reports

Click here for full text: PDF

Bifurcations in the Falkner Skan

Sparrow, Colin


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.

Back to Index

[Research] [News] [Tech Reports] [Palo Alto] [Bristol] [Japan] [Israel] [Site Map] [Home] [Hewlett-Packard]