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Units: Remarkable points in dynamical systems

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  • Gallas, Jason A.C.

Abstract

In number theory, “units” are very special numbers characterized by having their norm equal to unity. So, in the real quadratic field Z (√3) the number of −2 + √3 ≅ −0.2679491924… is a unit because (−2 + √3) (−2 - √3) = 1. In this paper we determine precisely the numerical values of the coordinates of some points defined by multiple intersections of domains of stability in the parameter space of the Hénon map and, in all cases considered for which analytical calculations were feasible, find that such intersection points are invariably defined by units and by simple functions of units. The very special points defined by units are analogous to the familiar multicritical points in phase diagrams. Some simple consequences of the precise dynamics on the ground fields enforced by the equations of motion are discussed.

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  • Gallas, Jason A.C., 1995. "Units: Remarkable points in dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 125-151.
    • Handle: RePEc:eee:phsmap:v:222:y:1995:i:1:p:125-151
    DOI: 10.1016/0378-4371(95)00265-0
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    References listed on IDEAS

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    1. Gallas, Jason A.C., 1994. "Dissecting shrimps: results for some one-dimensional physical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 196-223.
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    Cited by:

    1. Beims, Marcus W. & Gallas, Jason A.C., 1997. "Accumulation points in nonlinear parameter lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 238(1), pages 225-244.

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