Friday, March 14, 2008

First Post

Wikipedia has this topic: Polarization. The section "Basics: plane waves" has a 3-diagram demonstration of Linear, Circular and Elliptical polarization of light from an helical trajectory.

This may suggest that 3D helical are more powerful than 2D elliptical equations?

UCLA reports on the Double Helix Nebula observed by NASA's Spitzer Space Telescope and published in Nature.

Does this association with electromagnetism suggest that helices may serve as solenoids in general [or in mechanics as springs]?

Wikipedia discusses the Mathematics topic: Dynamical system classified as 37-xx by the Mathematics Subject Classification. This embraces many types of mathematics including ergodic and bifurcation theory. The latter contains Chaos Theory with attractors of various types such as Lorenz, Rossler and Smale's horseshoe and solenoid. The solenoid may be a helical torus having a prominent role in electrical engineering and serving as a spring in mechanical engineering?

I was surprised to learn that there exists an association of these attractors with Cantor sets when reading Hasselblatt and Katok A First Course in Dynamics: With a Panorama of Recent Developments.

I am surprised that there is not an AMS link suggested with 91-xx Game Theory, 93-xx Systems Theory or 49-xx Optimization?

Certainly the Ergodic pioneers John von Neumann minimax theorem and George David Birkhoff minimax periodic orbits have related although not necessarily identical ideas.

Perhaps electromagnetism is playing a dynamic game among energy and particles?