Symbolic Codes for Rotational Orbits

Abstract

Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-integrable limit, or alternatively from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consistent with numerical evidence. The resulting symbolic partition of the phase space consists of wedges constructed from images of the symmetry lines of the map.

47 pages, 23 figures

References in corpus (6)

• Generic Twistless Bifurcations
• Homoclinic Bifurcations for the Henon Map
• A generating partition for the standard map
• Symbolic Dynamics and Periodic Orbits for the Cardioid Billiard
• Computing periodic orbits using the anti-integrable limit
• Reversors and Symmetries for Polynomial Automorphisms of the Plane

Cited by in corpus (3)

• Syzygies in the two center problem
• Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps
• Anti-Integrability for 3-Dimensional Quadratic Maps