194 - Positive Lyapunov Exponents for Cat Map
194 - Positive Lyapunov Exponents for Cat Map
Presentation Slides (in progress) by Rita Pattaratornkosohn, Jonathan Parra, Atonio Thomas, Nikhil Gaitonde
Planned outline:
Week 1: Linear maps, norms, Lyapunov exponents
Week 2: SL(2,R), singular value decomposition, torus
Week 3: PSL(2,R) and RP^1
Week 4: Snippets of ergodic theory
Week 5: Cat Map and foliations
Week 6: Schrödinger operators
Week 7: Polar decomposition of Schrödinger operators
Week 8: Controlling directional derivatives
Week 9: Counting discontinuities and measuring the bad set
Week 10: Proving uniform positive Lyapunov exponents