PHYSICS SEMINAR
Limit Cycles and Hilbert's 16th Problem: The Poincaré-Bendixson Theorem
Dr. Lorne Nelson
Bishop's University
Friday, June 11, 2010
2:30 pm
Nicolls 315
Limit Cycles are a special class of periodic phenomena that are ubiquitous in nature (for example, the resting heartbeat of humans). But their existence is very difficult to ascertain using mathematical analysis. The preferred method to discover them involves the use of numerical algorithms (i.e., computers). However, there are many limitations in using computers since it is easy to overlook bona fide Limit Cycles because they can be found anywhere in what is generally an infinite phase space. In this talk I will review the very sparse amount of knowledge that we have learned about them in the past 130 years since they were first identified by Henri Poincaré. I will examine the implications of the Poincaré-Bendixson Theorem for the existence of Limit Cycles and show how Classical Novae (thermonuclear runaways on the surfaces of White Dwarf stars) can be viewed as the manifestation of a stable Limit Cycle.
