Analysis of high dimensional non-hyperbolic coupled systems through finite-time Lyapunov exponents

In this work, we investigate the relations among the Unstable Dimension Variability (UDV) and phase space dimensions in a coupled map lattice with diffusive coupling. Studying a simple system with UDV at low dimensions, we give theoretical support and numerical evidence to the statement that, from some fixed dimensional value onwards, there is no UDV. More precisely, we construct a high dimensional non-hyperbolic system without UDV.