Equivalence among orbital equations of polynomial maps
TLDR
In this paper, it was shown that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation and can be represented in an infinity of ways, all interconnected by certain nonlinear transformations.Abstract:
This paper shows that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic and valid for arbitrary dynamics governed by algebraic equations of motion.read more
Citations
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Field discriminants of cyclotomic period equations
TL;DR: In this article, it was shown that several orbital equations and orbital clusters of the logratic map coincide surprisingly with cyclotomic period equations, polynomials whose roots are Gaussian periods.
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Polynomial interpolation as detector of orbital equation equivalence
TL;DR: In this article, the 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 Tschirnhause.
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Field discriminants of cyclotomic period equations.
TL;DR: In this paper, 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, which sheds light into why numerical construction of databases is a hard problem.
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Preperiodicity and systematic extraction of periodic orbits of the quadratic map
TL;DR: In this paper, a polynomial mixing all 335 period-12 orbits has degree 4020, which is the degree of the polynomials whose degrees explode as the orbital period grows larger.
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Preperiodicity and systematic extraction of periodic orbits of the quadratic map
TL;DR: In this article, the authors used preperiodic points to systematically extract exact equations of motion, one by one, with no need for iteration, from the quadratic map of the orbital period.
References
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Journal ArticleDOI
The transitive groups of degree up to eleven
Gregory Butler,John McKay +1 more
TL;DR: In this article, the transitive groups of degree up to eleven were studied and a transitive transitive group up to 11 was proposed for algebraic geometry, which is the case in this paper.
Journal ArticleDOI
Dissecting shrimps: results for some one-dimensional physical models
TL;DR: In this article, the authors describe how certain shrimp-like clusters of stability organize themselves in the parameter space of dynamical systems and describe a family of models having the boundaries of all isoperiodic domains of stability totally degenerate.
BookDOI
An exploration of dynamical systems and chaos
TL;DR: In this paper, a mathematical introduction to dynamical systems is given, where the authors describe a dynamical system without dissipation, and a Dynamical system with dissipation and local bifurcation theory.
Journal ArticleDOI
Connection between Gaussian periods and cyclic units
TL;DR: In this article, it was shown that all known parametric families of units in real quadratic, cubic, quartic and sextic fields with prime conductor are linear combinations of Gaussian periods and exhibits these combinations.
Journal ArticleDOI
Automorphism group computation and isomorphism testing in finite groups
John Cannon,Derek F. Holt +1 more
TL;DR: A new method for computing the automorphism group of a finite permutation group and for testing two such groups for isomorphism is described.