Unitary Dynamics

1. Title of talk
2. Classical mechanics Example 1
3. Classical mechanics Example 2
4. Classical mechanics Example 3
5. Quantum mechanics
6. Possible questions
7. Describing the dynamics
8. Dynamics on sets (describing class. dyn.)
9. Dynamics on sets (different type of behav.)

Part 1: Topological entropy of a unitary operator

1. Generic singular continuity
2. Dynamics on the sc spectrum
3. Fourier transform of Cantor measure
4. Wiener, Percival and Co
5. Banach Spaces of measures
6. Rage theorems
7. Quantitative mixing rates
8. The Main result
9. The proof
10. Quantum Chaos?

Part 2: Discrete time quantum mechanics

1. Discrete time evolution
2. An example (Mathieu)
3. Time dependent version
4. Advantages of discrete time
5. Nonlinear discrete time evol
6. Why Discrete time evolution

Part 3: Schroedinger operators from twist maps

1. Standard map
2. Other Standard map
3. An integrable twist map?
4. An Anosov Standard map
5. The E=0 Standard map
6. From Standard map
7. From Anosov map
8. From Anosov map 2
9. From E=0 Standard map
10. From Circle map
11. Vague attractors
12. Different type of results

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