What's in a name? The original title of our book, Regular and Stochastic
Motion, was chosen to emphasize Hamiltonian dynamics and the physical
motion of bodies. The new edition is more evenhanded, with considerably
more discussion of dissipative systems and dynamics not involving
physical motion. To reflect this partial change of emphasis, we have
substituted the more general terms in our title. The common usage of the
new terms clarifies the emphasis of the book. The main change in the
book has been to expand the sections on dissipative dynamics, including
discussion of renormalization, circle maps, intermittancy, crises,
transient chaos, multifractals, reconstruction, and coupled mapping
systems. These topics were either mainly in the mathemati- cal
literature or essentially unstudied when our first edition was written.
The volume of work in these areas has surpassed that in Hamiltonian
dynamics within the past few years. We have also made changes in the
Hamiltonian sections, adding many new topics such as more general
transformation and stability theory, connected stochasticity in
two-dimensional maps, converse KAM theory, new topics in diffusion
theory, and an approach to equilibrium in many dimensions. Other
sections such as mapping models have been revised to take into account
new perspectives. We have also corrected a number of misprints and
clarified various arguments with the help of colleagues and students,
some of whom we acknowledge below. We have again chosen not to treat
quantum chaos, partly due to our own lack ofacquaintance with the
subject.
