Parametrized Dynamics of the Weierstrass Elliptic Function
Conformal Geometry & Dynamics
We study parametrized dynamics of the Weierstrass elliptic ℘ function by looking at the underlying lattices; that is, we study parametrized families ℘Λ and let Λ vary. Each lattice shape is represented by a point τ in a fundamental period in modular space; for a fixed lattice shape Λ = [1, τ] we study the parametrized space kΛ. We show that within each shape space there is a wide variety of dynamical behavior, and we conduct a deeper study into certain lattice shapes such as triangular and square. We also use the invariant pair (g2, g3) to parametrize some lattices.