Snail-like pattern generation with the Henon family of maps

In this paper we show that in the Henon family of maps x(n+1) = A + By(n) - x(n)(2), y(n+1) = x(n), for given parameter values, the orbit of an initia l segment has a snail-like pattern that is related to the starfish-like pat tern of the orbit of an initial point for the same parameter values. We stu dy the parameter plane in the Henon family of maps, searching for orbits wi th both starfish-like and snail-like patterns. (C) 2001 Elsevier Science Lt d. All rights reserved.