4 citations · 15 across the 14 of their papers we have counts for
14 papers
Points with Commuting Coordinates over Division Rings
Adam Chapman, Solomon Vishkautsan
We investigate the properties of multivariate polynomials evaluated at points with commuting coordinates over division rings and octonion algebras. Given a division ring , this…
General Polynomials and Eigenvalues Over Cayley--Dickson Algebras
Adam Chapman, Ilan Levin, Solomon Vishkautsan
In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic…
Recurrence relations over division algebras
Adam Chapman, Solomon Vishkautsan
We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials…
The field of iterates of a rational function
Francesco Veneziano, Solomon Vishkautsan
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definit…
Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras
Adam Chapman, Solomon Vishkautsan
Over a composition algebra , a polynomial has a root if and only for some . We examine whether this is true for general…
Roots and Critical Points of Polynomials over Cayley--Dickson Algebras
Adam Chapman, Alexander Guterman, Solomon Vishkautsan +1
We study the roots of polynomials over Cayley--Dickson algebras over an arbitrary field and of arbitrary dimension. For this purpose we generalize the concept of spherical roots fr…
Roots and Dynamics of Octonion Polynomials
Adam Chapman, Solomon Vishkautsan
This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polyn…
Fixed Points of Polynomials over Division Rings
Adam Chapman, Solomon Vishkautsan
We study the discrete dynamics of standard (or left) polynomials over division rings . We define their fixed points to be the points for which …
Quadratic rational functions with a rational periodic critical point of period 3
Solomon Vishkautsan, Michael Stoll
We provide a complete classification of possible graphs of rational preperiodic points of quadratic rational functions defined over the rationals with a rational periodic critical…
Scarcity of finite orbits for rational functions over a number field
J. K. Canci, Sebastian Troncoso, Solomon Vishkautsan
Let be a an endomorphism of degree of the projective line, defined over a number field . Let be a finite set of places of , including the archimedean place…
Scarcity of cycles for rational functions over a number field
J. K. Canci, Solomon Vishkautsan
We provide an explicit bound on the number of periodic points of a rational function defined over a number field, where the bound depends only on the number of primes of bad reduct…
Quadratic maps with a periodic critical point of period 2
J. K. Canci, Solomon Vishkautsan
We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rationa…
Residual periodicity on the Markoff surface
Solomon Vishkautsan
A case study of arithmetic dynamics over the rationals on the Markoff surface is presented, in particular the local-global dynamical property of strong residual periodicity. The dy…
Arithmetic dynamics on smooth cubic surfaces
Solomon Vishkautsan
We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field . In particular we are interested in the product of non-commu…