摘要：
Mathieu type dynamical systems are mappings or vector fields given by trigonometric polynomials. A phase-locked region of for a family of vector fields on a torus is the set of those values of the parameters for which the modulus of the scalar product (xi, g(t)x - x), where g(t) is the phase flow of the vector field, grows slower than the first power of t, as t --> infinity. It is shown that for Mathieu type vector fields on a torus, near to integrable ones, the asymptotics of the regions of the phase-locked regions depends on the spectrum of the trigonometric polynomial (or on its Newton polyhedron).
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