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A combinatorial model for reversible rational maps over finite fields
2009
Nonlinearity
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e., map-independent) distribution function R(x)=1-e^-x(1+x) has been conjectured to exist, for the normalized cycle lengths of the reduced map in the large field limit (J. A. G. Roberts and F. Vivaldi, Nonlinearity 18 (2005) 2171-2192). We show that these
doi:10.1088/0951-7715/22/8/011
fatcat:om7h5mmmevdxdkzbyszynnethq