F Vivaldi 1992 Nonlinearity 5 133 doi:10.1088/0951-7715/5/1/005
Geometry of linear maps over finite fields
F Vivaldi
Show affiliationsThe finite fields of degree two are reinterpreted as discrete phase spaces on the two-dimensional torus. The authors study dynamical systems obtained by iterating linear maps over these fields, from a geometrical viewpoint. These maps can be regarded as the two-dimensional discrete equivalent of a Bernoulli shift. They yield irregular motions, which may coexist with spatial order. They find that the dynamics of orbits of long period can be characterized as a percolation process. The question of randomness in dynamical systems over finite sets is discussed.
- PACS
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02.40.-k Geometry, differential geometry, and topology
- MSC
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37Cxx Smooth dynamical systems: general theory (See also 34Cxx, 34Dxx)
- Subjects
- Dates
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Issue 1 (January 1992)
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Geometry of linear maps over finite fields
F Vivaldi 1992 Nonlinearity 5 133
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