The self-rotation number, as defined by Peckham, is the rotation rate of th
e image of a point about itself. Here we use the notion of "turning angle"
to give a simplified algorithm to compute the self-rotation number for maps
that "avoid an angle". We show that the orientation preserving Henon map d
oes avoid an angle. Moreover, the self-rotation number for orbits of the He
non map can be computed once and for all at the anti-integrable limit by a
simple algorithm depending upon the symbol sequence for the orbit. (C) 2000
Elsevier Science B.V. All rights reserved. MSG: 58F05; 58F03; 58C15.