92-137 E.Bollt , J.Meiss

Breakup of Invariant Tori for the Four Dimensional Semi-Standard Map (57K, LaTeX, AMS fonts) Oct 16, 92

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Abstract. \begin{abstract} We compute the domain of existence of two-dimensional invariant tori with fixed frequency vectors for a four-dimensional, complex, symplectic map. The map is a generalization of the semi-standard map studied by Greene and Percival; it has three parameters, $a_1$ and $a_2$ representing the strength of the kicks in each degree of freedom, and $\epsilon$, the coupling. The domain of existence of a torus in $(a_1,a_2)$ is shown to be complete and log-convex for fixed $k = \epsilon/a_1 a_2$. Explicit bounds on the domain for fixed $k$ are obtained. Numerical results show that quadratic irrationals can be more robust than the cubic irrational, ``the spiral mean." \end{abstract}

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