Western States (Caltech) and Southwest (Tucson) 1996
Unitary Dynamics
Title of talk
Classical mechanics Example 1
Classical mechanics Example 2
Classical mechanics Example 3
Quantum mechanics
Possible questions
Describing the dynamics
Dynamics on sets (describing class. dyn.)
Dynamics on sets (different type of behav.)
Part 1: Topological entropy of a unitary operator
Generic singular continuity
Dynamics on the sc spectrum
Fourier transform of Cantor measure
Wiener, Percival and Co
Banach Spaces of measures
Rage theorems
Quantitative mixing rates
The Main result
The proof
Quantum Chaos?
Part 2: Discrete time quantum mechanics
Discrete time evolution
An example (Mathieu)
Time dependent version
Advantages of discrete time
Nonlinear discrete time evol
Why Discrete time evolution
Part 3: Schroedinger operators from twist maps
Standard map
Other Standard map
An integrable twist map?
An Anosov Standard map
The E=0 Standard map
From Standard map
From Anosov map
From Anosov map 2
From E=0 Standard map
From Circle map
Vague attractors
Different type of results
Oliver home