Breakup of invariant tori for the four-dimensional semi-standard map

作     者：Bollt, E.M. Meiss, J.D. 

作者机构：Program in Applied Mathematics Box 526 University of Colorado Boulder CO 80309 USA 

出 版 物：《Physica D: Nonlinear Phenomena》 (Physica D)

年 卷 期：1993年第66卷第3-4期

页      面：282-282页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：National Science Foundation, NSF, (DMS-9001103a) National Science Foundation, NSF Office of Naval Research, ONR, (NOO014-91-403W7) Office of Naval Research, ONR 

摘      要：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 ϵ, 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 = ϵ / 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.