Finding lower bounds in complexity theory has proven to be an extremely difficult task. We analyze three proofs of lower bounds that use heavy techniques from algebraic geometry through the lense of dynamical systems. Interpreting programs as graphings – generalizations of dynamical systems that model Girard's Geometry of Interaction, we show that the three proofs share the same structure and use algebraic geometry to give a bound on the topological entropy of the system representing the program. This work, joint with Thomas Seiller, aims at proposing Geometry of Interaction derived methods to study dynamical properties of models of computation beyond Curry-Howard.