UNIFIED DYNAMICAL SYSTEMS ON COARSE SPACES

The paper’s Theorem 3.17 states that if two coarse dynamical systems are (f,h)-coarse conjugate, then their induced set-valued systems on the coarse hyperspaces are (exp f,h)-coarse conjugate, with a brief proof that cites Proposition 3.14 (exp preserves bornologous/effectively proper/asymorphism) and notes exp f ∘ exp φ_g = exp φ̃_{h(g)} ∘ exp f . The model independently reconstructs the key functorial identity (exp f × exp f)(E^*) = ((f×f)(E))^* and uses it to prove that exp f is an asymorphism and that conjugacy lifts, thereby supplying details that the paper references to [21] but does not re-prove. Aside from minor notational slips in the paper (e.g., writing φ instead of exp φ in the theorem statement), the arguments agree in substance and conclusion .