Invariant Measures for the n-Dimensional Border Collision Normal Form

被引：5
作者：
Glendinning, Paul [1 ]
机构：
[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2014年 / 24卷 / 12期
基金：
英国工程与自然科学研究理事会;
关键词：
Border collision bifurcation; attractor; piecewise smooth systems; piecewise affine systems; MULTIDIMENSIONAL PIECEWISE AFFINE; BIFURCATIONS; ATTRACTORS; SMOOTH; MAPS;
D O I：
10.1142/S0218127414501648
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The border collision normal form is a continuous piecewise affine map of R-n with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence the attractors have Hausdorff (fractal) dimension n. If n = 2 the attractors have topological dimension two, i.e. they contain open sets, and if n > 2 then they have topological dimension n generically.
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页数：11
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