SERC School on Nonlinear Dynamics

PRL Ahmedabad. December 2004

Lecture Notes and Other Material of
Arul Lakshminarayan
Department of Physics
Indian Institute of Technology Madras
Chennai 600036.


Lecture Notes

All Lecture notes are PS files. This is substantially what were my notes for the ISI school
on Nonlinear Dynamics at Kolkata last year.
 
Lecture: 1 Lecture: 3 Lecture: 5
Lecture: 2 Lecture: 4 Lecture: 6

GIF Animations: Bush on the Arnold Cat Map

Click on the Bush pictures for a 10 frame trip of Bush through the toral automorphism,
the Arnold cat map. Use the browsers "Back" button to get back.
                                           

                                         

                                   
200 frames


About the Animation

  The animation loops infinitely, and so you see Dubya back, again and again and again. Click on the "200 frame" areas for a 200 frame animation (more than 4 MB ) of the left picture that does not loop at all. I would recommend downloading it and then viewing.

However here  we see the initial Bush reappearing after 192 frames, despite all the intervening chaos! Life, as we sadly know, imitates art. The cat map is a completely chaotic, reversible map, a toy model of  a two-degree of freedom chaotic Hamiltonian system.

In Lecture 3, you will find a description of how I made these animations.

More Below

I found a cool Java Applet for the Image processing of the Cat Map (and more), especially for those who would rather see Catherine Zeta Jones than Bush. See Below.

Java Applets

The Pendulum Laboratory of Franz-Josef Elmer
From the simple pendulum through resonances to the forced pendulum, one and half degree of freedom of systems, and an introduction to chaos. I have downloaded the whole lab, and so it is in a local area. You may do so as well, Elmer has kindly provided the entire caboodle. Good beginning.

The Chaos Demos and Writeups  of V. Balakrishnan, Suresh Govindarajan.
The Java codes were written by  Phani Kiran and Prabhu Ramachandran,
former B. Tech students of IIT Madras. This includes the cool Cat Applet I spoke of above.

Explore Time Evolution in 2-D Maps and Play Some  Billiards. The following Java codes were written by   Reddy and Vishnu (?),  former summer students at PRL Ahmedabad, and B. Tech students of computer science from IIT Guwahati. Unfortunately they have been so self-effacing, I cannot find their names on any of the programs or writeups they wrote several years ago.

Two-Dimensional Maps
Standard Map Henon Map                                                        

Two-Dimensional Billiards

Annular Billiards: Circle in a Circle.