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 history

• The current version is dated 2009-04-23. The only difference from the previous version is that some material has been moved to a more logical location. (See comments to previous version.)
• The current version is 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. (I did it this way to minimize confusion in the middle of the term. In a future version, the new chapter 7 will be added to or after chapter 1, and the new chapter 8 will be incorporated in 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. It is not unlikely that similar revisions will soon happen in the rest of the document. To print only the first chapter, print pages 1–7 of the A5 version or pages 1–4 of the A4 version.

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.