Dynamical Systems. Winter. 2018. UCSC.
Office hrs: Friday 1:15pm-2:50pm and by appt.

Class plan. I aim to have the class roughly half student run and student determined. This means that (ideally) half the lectures will be given by grad students. I will begin the first lecture or two with basics and an overview but expect students to jump in quickly and begin to give lectures.
Occassional Homework might be assigned and discussed.

Homework Homework & Solutions

references for student talks
a few recommended texts

INFO on homeos of the circle and rotation number: (thanks, Gabe! )
Ghys on Diff(S^1)
Ghys: knotted orbits from flows on 3-manifolds

groups acting on the circle (review)
elem notes on circle homeos good disc'n of rot'n number starting p. 31.

POSSIBLE TOPICS FOR TALKS. You may choose any topic in dynamical systems to speak on , subject to my approval. It is nice if you find your own topic. However, here are some ideas and papers for lecture topics.

Here are others, with some overlap. Proof of Poincare-Bendixson.
Proof of Stable Manifold Theorem.
Computation of Entropy for full shifts on k symbols.
Lorentz's paper
arXiv, Dynamical Systems most of the papers found here are appropriate
any of these: original Papers including Lorentz's.
works of Avilla; for example:
on the almost-Mathieu eqn with Jitomirskaya
or translation surfaces; Teichmuller dynamics
More around almost-Mathieu: Damanik survey -esque
Gole Symplectic Twist Map book
Wilkinson papers; eg:
A survey of Lyapanov exponents, ergodicity, in the Bulletin AMS. Good and current.
surveys by Etienne Ghys: Lorentz. modular groups....
How wierd can the equilibrium points be? :
Critical sets in 3-space Pugh and Grayson
Antoine’s necklance: explained, for example, in E Moise: Geometric Topology in dimensions 2 and 3: ch 12, 13,… on Cantor set, Antoine’s necklace.
Dec 28 2017: pseudorotations by Ginzburg and Gurel.
Rock Paper Scissors paper with lizards (Barry Sirnevo game) ************************************

Lecture Schedule


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Miscellaney. Sites to explore

another syllabus (Rick Moeckel's) examples of chaotic dynamics
attractors ************ BOOKS.
a book on circle action