Generalized Dynamical Ordering and Topological Entropy in the Henon Map
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Under area- and orientation-preserving maps, the images of the symmetry axes accumulate at the unstable manifold of a saddle fixed point P, while their inverse images accumulate at the stable manifold of P. Before or after the tangency of these stable and unstable manifolds, four types of generalized dynamical ordering are derived. They determine the order of the appearance of the symmetric periodic orbits. We derive these types of ordering for the area- and orientation-preserving Henon map. A lower bound of the topological entropy is obtained by using the symbol sequence of the periodic orbits included in the dynamical ordering and the trellis method.
- Progress of Theoretical Physics
Progress of Theoretical Physics 114(4), 763-791, 2005-10
Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan