标准非扭转映射中无剪切蜿蜒和“外部”环面的破裂

Breakup of shearless meanders and "outer" tori in the standard nontwist map.

作者信息

Fuchss K, Wurm A, Apte A, Morrison P J

机构信息

Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA.

出版信息

Chaos. 2006 Sep;16(3):033120. doi: 10.1063/1.2338026.

DOI:10.1063/1.2338026

PMID:17014225

Abstract

The breakup of shearless invariant tori with winding number omega=(11+gamma)(12+gamma) (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders [folded-over invariant tori which are not graphs over the x axis in (x,y) phase space], whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.

摘要

利用格林留数准则对标准非扭转映射中缠绕数为(\omega=(11 + \gamma)(12 + \gamma))（连分数表示）的无剪切不变环面的破裂进行了数值研究。这种缠绕数的环面可以呈现蜿蜒的形状[在((x,y))相空间中不是(x)轴上图形的折叠不变环面]，其破裂是这里关注的首要问题。其次，这种缠绕数的多个无剪切轨道可能存在，导致一种新型的破裂情形。在保面积映射的重整化群框架内讨论了结果。还研究了临界环面的正则性。