Modeling polarization for Hyper-NA lithography tools and masks
Kafai Lai, Alan E. Rosenbluth, et al.
SPIE Advanced Lithography 2007
InAdler et al [Convex dynamics and applications. Ergod. Th. & Dynam. Sys. 25 (2005), 321-352] certain piecewise linear maps were defined in terms of a convex polytope. When the convex polytope is a simplex, the resulting map has a dual nature. On one hand it is defined on RN and acts as a piecewise translation. On the other it can be viewed as a translation on the N-torus. What relates its two roles? A natural answer would be that there exists an invariant fundamental set into which all orbits under piecewise translation eventually enter. We prove this for N=1 and for acute and right trianglesi.e.non-obtuse triangles. We leave open the case of obtuse triangles and higher-dimensional simplices. Another question not treated is the connectivity of the invariant fundamental sets which arise. © 2009 Cambridge University Press.
Kafai Lai, Alan E. Rosenbluth, et al.
SPIE Advanced Lithography 2007
Andrew Skumanich
SPIE Optics Quebec 1993
Sankar Basu
Journal of the Franklin Institute
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering