On the Special Role of Symmetric Periodic Orbits in a Chaotic System

Details On the Special Role of Symmetric Periodic Orbits in a Chaotic System On the Special Role of Symmetric Periodic Orbits in a Chaotic System

1998-06-23

arxiv.org/abs/chao-dyn/9806024v1

Physica D 131 (1999) 254

Nonlinear Sciences

Chaotic Dynamics

17 pages, 5 PS-figures and 3 EPS-figures, uses elsart.cls and psfig.sty

Scientific paper

After early work of Henon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by discrete symmetries prove to be an important complement to the long known role of the orbits. The latter have particular importance in semi-classics. Based on the structural stability of hyperbolic horseshoes we give an argument that opens an avenue to the understanding of these facts.

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