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Sistemas dinĂ¡micos finitos booleanos monomiales afines
SepĂºlveda-Avendaño, Leonid B.
SepĂºlveda-Avendaño, Leonid B.
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Abstract
En este trabajo presentamos dos mĂ©todos para el estudio de la dinĂ¡mica de algunos sistemas discretos. Un mĂ©todo envuelve el estudio del comportamiento cĂclico de la dinĂ¡mica del sistema discreto lineal. El otro mĂ©todo presenta una nueva herramienta para el estudio de sistemas dinĂ¡micos discretos monomiales, usando la transformada discreta de fourier sobre Fq. La transformada discreta de fourier nos permite convertir un sistema multidimensional a uno unidimensional. Al final se resuelven dos problemas: determinar una cota superior para el nĂºmero de soluciones de f(x) =2 de un sistema monomial booleano afĂn f y tambiĂ©n contar el nĂºmero de ciertas involuciones sobre un cuerpo finito en tĂ©rminos de los residuos cuadrĂ¡ticos.
In this work we present two methods to study the dynamics of some finite dynamical systems. One method concerns the study of the cyclic behavior of the dynamics of a linear finite dynamical system. The other method concerns a way to transform a finite dynamical system, from a multidimensional to a unidimensional one. This last method is known as the discrete fourier transform over Fq. At the end, we solve two problems: we determine an upper bound for the number of solutions of f(x) =2 where f is an affine boolean monomial system, and we count the number of certain involutions over a finite field in terms of quadratic residues.
In this work we present two methods to study the dynamics of some finite dynamical systems. One method concerns the study of the cyclic behavior of the dynamics of a linear finite dynamical system. The other method concerns a way to transform a finite dynamical system, from a multidimensional to a unidimensional one. This last method is known as the discrete fourier transform over Fq. At the end, we solve two problems: we determine an upper bound for the number of solutions of f(x) =2 where f is an affine boolean monomial system, and we count the number of certain involutions over a finite field in terms of quadratic residues.
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2007
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Sistemas booleanos