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pro vyhledávání: '"Gallas, Jason A. C."'
Autor:
Gallas, Jason A. C.
We report extensive computational evidence that Gauss period equations are minimal discriminant polynomials for primitive elements representing Abelian (cyclic) polynomials of prime degrees $p$. By computing 200 period equations up to $p=97$, we sign
Externí odkaz:
http://arxiv.org/abs/2212.06115
Autor:
Gallas, Jason A. C.
Iteration of the quadratic map produces sequences of polynomials whose degrees {\sl explode} as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree $4020$, while for the $52,377$ period-20 orbits the degr
Externí odkaz:
http://arxiv.org/abs/2010.04013
Autor:
Gallas, Jason A. C.
Publikováno v:
Intern. J. Modern Physics C 31, 2050100 (2020)
Explicit formulas for {\sl orbital carriers} of periods $4$, $5$, and $6$ are reported for discrete-time quadratic dynamics. A systematic investigation of {\sl orbital inheritance} for periods as high as $k\leq 12$ is also reported. Inheritance means
Externí odkaz:
http://arxiv.org/abs/2008.01073
Autor:
Gallas, Jason A. C.
Publikováno v:
International Journal of Modern Physycs C, Feb 2020
We study monogeneity in {\sl period equations}, $\psi_e(x)$, the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic $\psi_e(x)$ of degrees $4 \leq e \leq 250$ are determined for extended intervals of pr
Externí odkaz:
http://arxiv.org/abs/2002.04445
Autor:
Gallas, Jason A. C.
We show that several orbital equations and orbital clusters of the quadratic (logistic) map coincide surprisingly with cyclotomic {\it period equations}, polynomials whose roots are Gaussian periods. An analytical expression for the field discriminan
Externí odkaz:
http://arxiv.org/abs/1912.06921
Autor:
Gallas, Jason A. C.
During the last six years or so, a number of interesting papers discussed systems with line segments of equilibria, planes of equilibria, and with more general equilibrium configurations. This note draws attention to the fact that such equilibria wer
Externí odkaz:
http://arxiv.org/abs/1909.05727
Autor:
Brison, Owen J., Gallas, Jason A. C.
Publikováno v:
International Journal of Modern Physics C 29 (2018)
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard {\sl poly
Externí odkaz:
http://arxiv.org/abs/1810.02312
Autor:
Gallas, Jason A. C.
Publikováno v:
International Journal of Modern Physics C 29 (2018)
This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Fi
Externí odkaz:
http://arxiv.org/abs/1809.05399
Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations contin
Externí odkaz:
http://arxiv.org/abs/1707.06947
Autor:
Gallas, Jason A. C.
This note records a curious numerical identity: the number 1318, connected with Vandermonde's cyclotomic quintic, may be decomposed in two distinct ways as a sum of products of pairs of numbers taken from the set \{$6, 16, 26, 41$\}, namely $1318 = 6
Externí odkaz:
http://arxiv.org/abs/0812.4850