Field discriminants of cyclotomic period equations

Jason A. C. Gallas
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Jason A. C. Gallas: Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, 58039-190 João Pessoa, Brazil2Complexity Sciences Center, 9225 Collins Ave. 1208, Surfside FL 33154, USA3Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 02, 1-20

Abstract: We show that several orbital equations and orbital clusters of the quadratic (logistic) map coincide surprisingly with cyclotomic period equations, polynomials whose roots are Gaussian periods. An analytical expression for the field discriminant of period equations is obtained and applied to discover and to fill gaps in number field databases constructed by numerical search processes. Such expression allows easy assess to inessential divisors of conventional discriminants and sheds light into why numerical construction of databases is a hard problem. It also provides significant information about the organization of periodic orbits of the quadratic map.

Keywords: Quadratic dynamics; symbolic computation; algebraic dynamics (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500217

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