Hyperbolic Amoebas

Amoebas are defined as images of sub-varieties of the algebraic torus under the coordinate-wise logarithmic map. The natural habitat of an amoeba in this case is the ordinary Euclidean space. We consider an analog of the logarithmic map for which amoebas live in the hyperbolic 3-space. I will describe the main similarities and differences between the usual and hyperbolic (co)amoebas.