Robust Ergodic Chaos in Discounted Dynamic Optimization Models

It is by now well-known that a variety of models in economics gives rise to discrete time, non-linear processes of the form(1.1)% MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa % aaleaacaWG0bGaey4kaSIaaGymaaqabaGccqGH9aqpcaWGObGaaiik % aiaadIhadaWgaaWcbaGaamiDaaqabaGccaGGPaaaaa!3F33!$$ {x_{t + 1}} = h({x_t}) $$ where the function h satisfies the Li-Yorke condition for “chaotic” or “complex” behavior. Besides the relative abundance of examples of chaos, yet another theme has rightly been stressed: quite simple models of economic theory may lead to such examples.