Nonlinear Systems an overview P510 F18

Tu-Th 9:30-10:50 in 222 LLP (tentatively)

The course will cover standard introductory materials required for the nonlinear dynamics course, but we will go far beyond elementary discussions on dynamical systems, complexity and complex systems.

A fairly complete set of lecture notes will be distributed.

My old book The Nonlinear World (Springer 2013, original U Tokyo Press 2009, 2015 (manuscript 1996); you can get e-book for free from our library) discusses many topics listed below, but the book is not at all elementary, so will never be used as a textbook.

The following topics will likely be included (no logical order in the list):

Three-body problem. KAM theorem, 1D map, chaos, Poincare section, Sarkovski sequence, Bernoulli, Anosov, Axiom-A, SRB measure, Cartwright-Littlewood, Smale horseshoe, Ruelle-Takens theorem, Takens reconstruction theorem, fluid examples, billiards, Markov partition and tracing property, Kolmogorov-Sinai entropy, Rokhlin’s formula, Shannon-McMillan-Breiman theorem, topological entropy, thermodynamic formalism, Ornstein’s theorem, ergodicity and mixing, symbolic dynamics, bifurcation, catastrophe theory, reductive perturbation and RG for differential equations, multifractals, Hausdorff dimension, Lyapunov spectrum and Pesin-Ruelle, Brin-Katok, Church-Turing thesis, (Universal) Turing machine, Kolmogorov complexity, Computability and physics, P-NP, von Neumann’s self-reproducing automata, complete integrability and inverse scattering, Painleve test, solitons, .........

Hopefully, each topic should consist of three parts: (1) intuitive explanation with illustrations; (2) theoretical physicist style justification, (3) where you can find respectable math.

Probably 5-6 HW 40 % Take-home mid term 40 % + capping final 20%

I wish you to get familiar with various mathematical and philosophical concepts, but hate grading.