CSSS 2008 Argentina-Readings

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Week 1

definition of chaos; examples in various fields an extended example: the logistic map - in that context, introduce:

 - bifurcations
 - bifurcation diagram and its structure, incl. Feigenbaum number
 - fractals and their connection to chaos

- continuous-time dynamics: definition - introduce concepts: state variables, state space, trajectory, initial

 condition, transient, attractor, basin of attraction, fixed point, stability,
 bifurcation, parameter

- an extended example: the Lorenz system

 - history, physical meaning
 - trajectories, attractors, bifurcations (give examples & reiterate definitions)
 - types of attractors
 - stability: definition & mathematics, incl. eigenstuff, un/stable manifolds
 - Lyapunov exponent and the connection to chaos

- numerical solvers: roles and issues - shadowing - projection vs section - Poincare sections in space & time - delay-coordinate embedding - examples: roulette, the SFI competition - applications:

 - filtering
 - control of chaos
 - synchronization & communication
 - spacecraft orbits
 - chaos in the solar system
 - harnessing the butterfly effect in fluids