Kenneth S. Jacobs

activity

20142018

most citedAn Equidistribution Result For Dynamical Systems on the Berkovich Projective Line

8 citations · 11 across the 3 of their papers we have counts for

collaborators

6 papers

math.DS2018

Hyperbolic Equivariants of Rational Maps

Kenneth Jacobs

Let $K$ denote either $R$ or $C$ . In this article, we introduce two new equivariants associated to a rational map $f \in K (z)$ . These objects naturally live on a r…

math.DS2016★ 3 cited

Iteration and the Minimal Resultant

Kenneth Jacobs, Phillip Williams

Let $K$ be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let $φ \in K (z)$ have degree $d \geq 2$ . We characterize maps for whic…

math.DS2015

Lower Bounds for non-Archimedean Lyapunov Exponents

Kenneth Jacobs

Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $P^{1}$ denote the Berkovich projective line over $K$ . The Lyapunov exponent for a rationa…

math.NT2015

Configuration of the Crucial Set for a Quadratic Rational Map

John R. Doyle, Kenneth Jacobs, Robert Rumely

Let $K$ be a complete, algebraically closed non-archimedean valued field, and let $φ (z) \in K (z)$ have degree two. We describe the crucial set of $φ$ in terms of the multipliers of…

math.DS2015

Quantitative Logarithmic Equidistribution of the Crucial Measures

Kenneth Jacobs

Let $K$ be a algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value. Let $ϕ \in K (z)$ with $deg (ϕ) \geq 2$ . In this…

math.DS2014★ 8 cited

An Equidistribution Result For Dynamical Systems on the Berkovich Projective Line

Kenneth Jacobs

Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $ϕ \in K (z)$ with $deg (ϕ) \geq 2$ . In this paper we consider the family of functions $\te…