Self-rotation number using the turning angle

The self-rotation number, as defined by Peckham, is the rotation rate of the 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 Hénon map does avoid an angle. Moreover, the self-rotation number for orbits of the Hénon 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.