THE CRITICAL FUNCTION FOR THE SEMISTANDARD MAP

被引：84
作者：
DAVIE, AM
机构：
[1] Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, EH9 312, Kings Buildings, Mayfield Road
来源：
NONLINEARITY | 1994年 / 7卷 / 01期
关键词：
D O I：
10.1088/0951-7715/7/1/009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the semistandard map F(x, y) = (x + y + ie(ix), y + ie(ix)), we consider the critical function K(ss)(omega), defined as the radius of convergence of a series expansion of a complex invariant curve of rotation number omega, and show that log K(ss)(omega) + 2SIGMAq(k)-1 log q(k+1) is bounded on the set of omega where it is well-defined, where {q(k)} are the denominators of the convergents to the real number omega. We discuss the implications for critical functions for the standard map.
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页码：219 / 229
页数：11
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