On the special role of symmetric periodic orbits in a chaotic system

After early work of Henon it has become folk knowledge that symmetric perio dic orbits are of particular importance. We reinforce this belief by additi onal studies and we further find that invariant closed symplectic submanifo lds caused by discrete symmetries prove to be an important complement to th e long known role of the orbits. The latter have particular importance in s emi-classics. Based on the structural stability of hyperbolic horseshoes we give an argument that opens an avenue to the understanding of these facts. (C) 1999 Published by Elsevier Science B.V. All rights reserved.