This paper studies the global equilibrium dynamics implied by a Lucas’ tree asset pricing model where the representative agent is subject to temptation in consumption choices, and displays dynamic self-control preferences, as defined by Gul and Pesendorfer [(2004) Econometrica 72, 119–158.]. It shows that endogenous cycles of period 2 and higher, as well as chaotic dynamics exist provided temptation utility is sufficiently important (with respect to standard commitment utility) and sufficiently convex. For parameterizations leading to complex deterministic dynamics, a stochastic version of the model admits rational expectations equilibria displaying excess volatility with respect to the underlying fundamentals.

We present an analysis of the reliability of computation of maximum Characteristic Exponents of Lyapunov from the numerical integrations of asteroid orbits over finite intervals of time. We used two complementary approaches - a comparison of the LCE estimates from the backward and forward integrations of orbits, and a comparison of the estimates coming from the integrations of the same initial conditions over different time spans. The main conclusion is that for a vast majority of asteroids ($> 80\%$) the results can be considered as reliable enough to reveal the very nature and basic properties of the motion.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

This paper discusses the asymptotic behavior of distributions of state variables of Markov processes generated by first-order stochastic difference equations. It studies the problem in a context that is general in the sense that (i) the evolution of the system takes place in a general state space (i.e., a space that is not necessarily finite or even countable); and (ii) the orbits of the unperturbed, deterministic component of the system converge to subsets of the state space which can be more complicated than a stationary state or a periodic orbit, that is, they can be aperiodic or chaotic. The main result of the paper consists of the proof that, under certain conditions on the deterministic attractor and the stochastic perturbations, the Markov process describing the dynamics of a perturbed deterministic system possesses a unique, invariant, and stochastically stable probability measure. Some simple economic applications are also discussed.

We have integrated the motion of the four Jovian planets on Myr timescales in fictitious solar systems in which the orbits differ from those of the real solar system. A change of ≲1% in the major axis of any one of the planets from its real value can lead to chaotic motion with a Lyapunov exponent larger than 10-5 yr−1. A survey of fifty solar systems with initial conditions chosen at random from a reasonable probability distribution shows the majority of them to be chaotic.