Franco Vivaldi

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We show that the dynamics of a birational map on an elliptic curve over a field is, typically, conjugate to addition by a point (under the associated group law). When the field is taken to be the function field of rational complex functions of one variable, this amounts to an algebraic geometric version of the Arnold– Liouville integrability theorem for(More)
We reduce planar measure-preserving rational maps over finite fields, and study their discrete dynamics. We show that application to the orbit analysis over these fields of the Hasse-Weil bound for the number of points on an algebraic curve gives a strong indication of the existence of an integral for the map. Moreover, the method is ideally suited to(More)
AMS Subject Classi cation: 58F20, 60J60, 65G05 We investigate the effects of round-off errors on quasi-periodic motions in a linear symplectic planar map. By discretizing coordinates uniformly we transform this map into a permutation of Z2 , and study motions near infinity, which correspond to a fine discretization. We provide numerical evidence that all(More)
We investigate the reduction to finite fields of polynomial automorphisms of the plane, which lead to invertible dynamics (permutations) of a finite space. We provide evidence that, if the map of the plane is non-integrable, then the presence or absence of a type of time-reversal symmetry called R-reversibility produces a clear signature in the cycle(More)
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(More)