- Coupled Map Lattices for nonstationary maps
Consider an infinite lattice (say, integers). At each site, there is a 1D time-dependent dynamical system that possesses some statistical memory loss property. Between the lattice sites, the spatial interaction is diffusive (which means that the interaction is close to identity) and of finite range (one site can only influence finitely many sites around it). One simple case of this setting is diffusive coupling of nearest neighbors. Our goal is to extract the memory loss property of the infinite lattice.
- Quasistatic Dynamical Systems with higher-dimension nonstationary maps
The idea of quasistatic dynamical systems (QDS) is borrowed from thermodynamics where the system's thermodynamic process changes infinitessimally small so that at any point, the system remains at equilibrium. Mikko Stenlund introduces this idea to dynamical systems using a triangular array of smooth expanding circle maps and a curve that traverses through it. We want to recover the quasistatic ergodic theorem with piecewise expanding maps.