Self-rotation number using the turning angle

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.