CUBO A Mathematical Journal Vol.13, N°01, (25–43). March 2011

CONTENTS

 

Evolutionary method of construction of solutions of polynomials and related generalized dynamics

 

Robert M. Yamaleev

Facultad de Estudios Superiores, Universidad Nacional Autonoma de Mexico, Cuautitlán Izcalli, Campo 1, C.P.54740, México. Joint Institute for Nuclear Research, LIT, Dubna, Russia. email: iamaleev@servidor.unam.mx

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ABSTRACT

Invariant theory as a study of properties of polynomials under translational transformations is developed. Class of polynomials with congruent set of eigenvalues is introduced. Evolution equations for eigenvalues and coefficients remaining the polynomial within proper class of polynomials are formulated. The connection with equations for hyper-elliptic Weierstrass and hyper-elliptic Jacobian functions is found. Algorithm of calculation of eigenvalues of the polynomials based on the evolution process is elaborated. Elements of the generalized dynamics with n-order characteristic polynomials are built.

Keywords: Nonspreading mapping, maximal monotone operator, inverse strongly-monotone mapping, fixed point, iteration procedure

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RESUMEN

La teoría de invariantes es un estudio de las propiedades de los polinomios que se desarrolla en las transformaciones de traslación. Se introduce una clase de polinomios congruentes con un conjunto de valores propios. Se formulan ecuaciones de evolución de los valores propios y los coeficientes del polinomio restante dentro de la clase adecuada de los polinomios. Se encuentra la conexión con las ecuaciones de Weierstrass hiperelípticas y funciones jacobiano hiper-elíptica. Son elaborados algoritmos de cálculo de valores propios de los polinomios basado en el proceso de evolución.

Mathematics Subject Classification: 12Yxx

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Received: February 2009.

Revised: September 2009.