10 papers
Orbit counting in polarized dynamical systems
Wade Hindes
We extend recent orbit counts for finitely generated semigroups acting on to certain infinitely generated, polarized semigroups acting on projective varieties. We th…
Counting points of bounded height in monoid orbits
Wade Hindes
Given a set of endomorphisms on , we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refi…
Dynamical and arithmetic degrees for random iterations of maps on projective space
Wade Hindes
We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height g…
Finite orbit points for sets of quadratic polynomials
Wade Hindes
Let be a set of quadratic polynomials with rational coefficients, and let be a rational basepoint. We classify the pairs for whi…
Stochastic Canonical Heights
Vivian Olsiewski Healey, Wade Hindes
We construct height functions defined stochastically on projective varieties equipped with endomorphisms, and we prove that these functions satisfy analogs of the usual properties…
Riccati equations and polynomial dynamics over function fields
Wade Hindes, Rafe Jones
Given a function field and , we study two finiteness questions related to iteration of : whether all but finitely many terms of an orbit of must possess a pri…