Most of the dynamical systems studied in this book are either three-dimensional flows or one- or two-dimensional maps. Common examples of maps and flows are listed on the previous page.
Flows are specified by differential equations (section 4.2.1). Similarly, maps are specified by difference equations:
Maps can also be written as 
.
The notation 
is read as ``maps to.''
The forward orbit of 
is
, where 
is the nth
composite of 
,
and 
is the identity function.
If the inverse 
is well
defined, then the backward orbit of is
.
Finally, the orbit of
is the sequence of all positions visited by , 
.