Symbolic Codes for Rotational Orbits

Details Symbolic Codes for Rotational Orbits Symbolic Codes for Rotational Orbits

2004-08-06

arxiv.org/abs/nlin/0408015v1

SIADS, 4:515--562,2005

Nonlinear Sciences

Chaotic Dynamics

47 pages, 23 figures

Scientific paper

10.1137/040612877

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.

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