Period Doubling in Four-Dimensional Volume-Preserving Maps

Details Period Doubling in Four-Dimensional Volume-Preserving Maps Period Doubling in Four-Dimensional Volume-Preserving Maps

1994-02-23

arxiv.org/abs/cond-mat/9402099v1

Physics

Condensed Matter

16 pages + 2 PostScript figures, RevTex 3.0, KWNU-SP-94-1

Scientific paper

We numerically study the scaling behavior of period doublings at the zero-coupling critical point in a four-dimensional volume-preserving map consisting of two coupled area-preserving maps. In order to see the fine structure of period doublings, we extend the simple one-term scaling law to a two-term scaling law. Thus we find a new scaling factor $\delta_3$ $(=1.8505\dots)$ associated with scaling of the coupling parameter, in addition to the previously known scaling factors $\delta_1$ $(=-8.7210\dots)$ and $\delta_2$ $(=-4.4038\dots)$. These numerical results confirm the renormalization results reported by Mao and Greene [Phys. Rev. A {\bf 35}, 3911 (1987)].

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