29-009 Spring 99

Part 1: Determinism, Chance and Chaos

Yannick Meurice
Dpt. of Physics and Astr., Univ. of Iowa, Iowa City, Iowa 52242, USA

Abstract:

These are informal lectures notes for the beginning of the course Directions in Modern Physics The following concepts are introduced with examples: deterministic evolution, stable and unstable equilibrium, irrational numbers, ergodicity, sensitive dependence on the initial conditions (``chaos''), randomness and the notion of a ``strange attractor''. The following examples will be used: linear maps, according to Newton, Translations on a circle, Linear motions on a torus, The quadratic map, Random number generators and Henon's map.

• Simple Examples of Dynamical Systems
  • Introduction
  • Linear Maps
  • The Square Root of 2
  • Uniform Circular Motion Observed at Stroboscopic Times
  • Two Independent Uniform Circular Motions.
  • A Quadratic Map of the Interval [-1,1]
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