Limit cycles for successive projections onto hyperplanes in ℝn

James Angelos, George Grossman, Edwin Kaufman, Terry Lenker, Leela Rakesh

Research output: Contribution to journalArticlepeer-review

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In this paper we consider successive orthogonal projections onto m hyperplanes in ℝn, where m ≥ 2 and n ≥ 2. A limit cycle is defined to be a sequence of points formed by projecting onto each of the hyperplanes once in a prescribed order, with the last projection giving the starting point. Several examples, including triangles, quadrilaterals, regular polygons, and arbitrary collections of lines in ℝ2, are solved for the limit cycle. Limit cycles are found in various ways, including by a limiting process and by solving an mn × mn linear system of equations. The latter approach will produce all the limit cycles for an arbitrary ordered set of m hyperplanes in ℝn.

Original languageEnglish
Pages (from-to)201-228
Number of pages28
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - Dec 1 1998


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