FMA140: Olinjära dynamiska system -- Nonlinear dynamical systems



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Kursmaterial - Course material

Main book

The file Lecture Notes revised 121214 contains the Lecture Notes I will use along the course, including some exercises, that are part of the course.

Suggested excercises from the Lecture Notes.

Chapter 1: 1.1, 1.2, Appendix A.7, A.8
Chapter 2: 2.1--2.3, 2.9--2.11
Chapter 3: 3.2, 3.3, 3.5, 3.7, 3.8--3.11
Chapter 4: 4.1--4.6, 4.11-4.13
Chapter 5: 5.1--5.3, 5.8--5.11
Chapter 6: 6.1--6.3
Chapter 7: 7.1--7.3
Chapter 8: 8.1--8.6, Appendix A1--A.5
Chapter 9: 9.1--9.5 are almost solved in the Notes.
There is nothing wrong with trying other exercises from the Lecture Notes as well. Answers are not available but some suggestions are given on Appendix B of the Lecture Notes.

Additional material

Phase-portrait of linear 2-d dynamical systems (ODE's).
On the eigenvalues of 2x2 matrices.Useful for Home exercise nr 2 (now incorporated to the main text of the LN).
Om inversa funktionssatsen -- About the Inverse function theorem
Recepttillägg till centralamångfaldssatsen -- Recipe for central manifold computations.



Literature

Apart from the Lecture Notes to be delivered along the course you may consider reading the following book, which is more applications oriented.
oo H.G. Solari, M. A. Natiello and B.G. Mindlin,
Nonlinear Dynamics: A Two-way Trip from Physics to Math,
Institute of Physics, UK, 1996.
Use the book's ISBN number for searching: 0750303808.
The editor (Taylor and Francis) sells the book directly but other booksites may occasionally be cheaper. Ask e.g. www.bokfynd.nu to get different prices.
The book has a number of misprints. Some of them have been discovered, other are waiting for a keen and accurate reader. The updated known list of misprints is here.



Interesting references for the research-oriented student

T-Y Li and J Yorke, Period Three Implies Chaos, Amer. Math. Monthly, 82, 985, (1975).
L Block, J Guckenheimer, M Misiurewicz, L-S Young, Periodic Points and Topological Entropy of One Dimensional Maps, Lecture Notes in Mathematics 819, 18, Z. Nitecki and C. Robinson (eds), Springer, 1980.