Part of the
Progress in Mathematics
book series (PM, volume 200)
In nonlinear dynamics without symmetry there is a hierarchy of increasingly complicated dynamic behavior: steady-state, equilibrium, periodic, quasiperiodic, chaotic. See Ruelle and Takens  and Broeret al.
. So far we have studied analogous behavior for steady, periodic, and quasiperiodic states of equivariant differential equations, asking the following questions:
What symmetry groups, in principle, might states have?
What are the general existence and stability theorems?
what this book tries not to do
What is the interpretation in physical space of the symmetric dynamics found in phase space?
We now ask similar questions for chaotic solutions of equivariant dynamical systems.
KeywordsInvariant Measure Chaotic Attractor Isotropy Subgroup Ergodic Measure Chaotic Saddle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.