BGU Physics Department


Introduction to Nonlinear Dynamics

Course number: 203-2-4721
4 hours, 3.5 points


Lecturer:Yair Zarmi

Lectures / Classes / Reception hours:

Day
Time
Building / Room
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Policy:

The grade is combined as follows: 50% based on a small project (10-15 pages, the topic suggested either by the student or by the lecturer) and 50% on problems in the lecture notes, as well as problems given in class. All the works submitted by the students will be checked, so that the grade on the problem part is an average grade on all the problem solutions that have been submitted.

Syllabus (from the Shnaton site):

Sources and links:

Course structure

No. Topic Week Source
1 Introduction - The richness of the nonlinear world 1-2
2 Basic concepts, Stability of solutions 3
3 Error estimates and secular terms in perturbation expansions 4
4 The method of Normal Forms 5-6
5 The method of multiple time scales 7-8
6 The logistic equation and the route to Chaos 9
7 Fundamental concepts in Fractals and Chaos 10
8 Nonlinear wave equations 11-12
9 Special topics (Current research problems, new concepts) 13


Lecture notes

  1. Introduction
  2. Basic concepts
  3. Stability of solutions
  4. Error estimates in perturbation expansions
  5. Secular terms
  6. Normal Forms & Lie transformations
  7. Poincaré-Lindstedt expansion method
  8. Method of averaging
  9. Second-order averaging
  10. Averaging in periodic systems
  11. Method of multiple time scales
  12. Special issues in perturbation analysis

Additional material