The Henon Map

Hi guys,

I am studying dynamical systems in my spare time. Currently, I am writing software, and trying to learn more about the Henon map. Anyone have any experience in this area or in dynamical systems in general?

Chris

Hello
I have an interest in "complexity theory" especially from the philosophical side. I have taken college math through calculus, differential equations and complex analysis though I had difficulties with these subjects. But it seems that those difficulties plus early love of math has driven me to keep thinking about math ideas all my long life-I'm 67. In addition to dynamical systems I am interested in quantum mechanics and the contemplation of "theories of everything". I am also working for fun on a long term assembly language program for the calculation of quaternions.

jwgrace@rcn.com wrote:Hello
I have an interest in "complexity theory" especially from the philosophical side. I have taken college math through calculus, differential equations and complex analysis though I had difficulties with these subjects. But it seems that those difficulties plus early love of math has driven me to keep thinking about math ideas all my long life-I'm 67. In addition to dynamical systems I am interested in quantum mechanics and the contemplation of "theories of everything". I am also working for fun on a long term assembly language program for the calculation of quaternions.

Welcome to the forum. Very interesting subjects. I have a masters degree, which for almost any subject in math, means that I have heard of it, but don't know a great deal about it. Like the old saying, Jack of all trades, Master of none. Quarternions have always interested me, and I did some work with them in my Algebra class studying them as a group and the operations on the group. But I still know very little. I would love to know more about your work with them.

My interest in Quaternions was more recently piqued by the book "Quaternions and Rotation Sequences" by Jack B. Kuipers. My over all interest comes about because a Quaternion collapses into a Complex object when two of the three "imaginary" axes = 0. The "complex object collapses into a real object when i=0. Shades of tensors collapsing into vectors collapsing into scalars. Which gets into physics and the relationship of mathematics to the real world. I am always fascinated by the vector cross product which creates the resultant vector emerging at a 90 degree angle from the plane of the two vectors. Just like electricity and magnetic fields. And quaternions are now usually used as the 3 unit vectors signifying 3 dimensional direction. One of my desires is to study nonlinear objects generated by complex algebra or quaternion algebra such as the Mandelbrot Set. In specific, I am interested in drilling all the way down into the self similarities to find out if the self similarities remain as predicted. However in the world of continuous mathematics, you never come to the end of drilling down. But suppose you assume a universe where space and time itself is quantized and there becomes a minimum for each that is limited by quantum numbers. a la physicist Lee Smolin's idea (perhaps now discarded). Then in order to handle the physical functions like acceleration=L squared/t squared we would need about 1000 bits for the numerals. For this I am working out quaternion arithmetic. Each number is represented by 16 64bit words. And a quaternion has 4 numbers, and a quaternion multiplication has 16 products. Just the opportunity to learn how to program multi threaded programs. And behind all of this is the philosophical qustion of the relationship of mathematics to the real world. Enough for tonight.