Assorted notes on dynamical systems
Notes created for a course on Differential equations and dynamical systems. I wrote these up as separate notes for the spring term of 2007; for the spring term of 2008, I have collected the notes into one document.
The main book for the course is Jordan & Smith's Nonlinear Ordinary Differentical Equations. These notes serve as a supplement.
To view or download
Best for on-screen viewing: A5 size (PDF).
Best for printing: A4 size (PDF).
(If you need to print on US letter paper, be sure to ask your printer driver to reduce the size to fit the paper.)
- Version dated 2016-03-31 (current version). Fixed a typo: Poincaré–Bendixson requires n=2!
- Version dated 2012-03-18 (this version was never posted here). Altered the uniqueness proof. Corrected a typo.
- Version dated 2009-04-23. The only difference from the previous version is that some material has been moved to a more logical location.
- Version dated 2009-04-21. Changes: Improved the statement and proof of Theorem 3. In chapter 2, the argument for the saddle case is improved. New chapter 7 on the flow. New chapter 8, an addendum to chapter 3. There are some cosmetic changes, including the addition of hyperlinks.
- Version dated 2009-01-12. The only differences from the 2009-01-11 versionappear on pages 6 and 7 (3 and 4 in the A4 version): A misprint on page 7 line 8, plus alignment of misaligned formulas.
- Version dated 2009-01-11. The only difference from the 2008-04-03 version results from a change in a documentclass file getting rid of a bad page break.
- Version dated 2008-04-03. I added two new results on page 18. This has pushed later material up to a page further back.
- Version dated 2008-01-24. There are no major changes, but the uniqueness proof for ODEs has been improved. There are various other minor improvements as well.
- Version dated 2008-01-11: The first chapter, on well-posedness, has been substantially rewritten compared to the original note.
Please respect the copyright
The notes may be freely copied for personal or classroom use; contact me if you wish to copy them for any other reason.