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Asymptotic expansions of unstable (stable) manifolds in time-discrete systems

Shin-itiro Goto·Kazuhiro Nozaki
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Abstract

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative Hénon map, both of which exhibit the strong homoclinic chaos. In terms of the asymptotic expansion, a simple formulation is presented to give the first homoclinic point in the double-well map. Even a truncated expansion of the unstable manifold is shown to reproduce the well-known many-leaved (fractal) structure of the strange attractor in the Hénon map.

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BibTeXRIS

Shin-itiro Goto, Kazuhiro Nozaki. 1999-10-18. Asymptotic expansions of unstable (stable) manifolds in time-discrete systems. https://arxiv.org/abs/chao-dyn/9910025

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