K.T. Alligood, T.D. Sauer and J.A. Yorke:
Chaos, an Introduction to Dynamical Systems
(Springer, New York 1996). An elegant introduction to maps,
chaos, period doubling, symbolic dynamics, fractals, dimensions. A
good companion to this webbook.
E. Ott:
Chaos in Dynamical Systems
(Cambridge, 1993).
As above, with baker's map used to illustrate many key techniques in
analysis of chaotic systems. Perhaps harder than the above two as
the first book on nonlinear dynamics.
The introductory course should give students skills in qualitative and
numerical analysis of dynamical systems for short times (fixed points,
bifurcations) and familiarize them with Cantor sets and symbolic
dynamics for chaotic dynamics. With this, and graduate level exposure
to statistical mechanics, partial differential equations and
quantum mechanics, the stage is set for any of the 1-semester advanced
courses based on this webbook.
Each course starts with the
introductory chapters on qualitative dynamics, symbolic dynamics and
flows.