La astucia de Mangue Evuna

Autor y título sacados de la cubiertaApoyo prestado en la ilustración y difusión por el Centro Cultural Español de Malabo y la FAOPremios: Primer premio en el I Concurso Literario "Cuentos y relatos para conservar el medio ambiente" en la VI Semana de la Biodiversidad (Malabo, mayo 2017

NONLINEAR DYNAMICS AND CHAOS PART II: ERGODIC APPROACH

This is the second part of a two-part survey of the modern theory ofnonlinear dynamical systems. We focus on the study of statisticalproperties of orbits generated by maps, a field of research known asergodic theory. After introducing some basic concepts of measuretheory, we discuss the notions of invariant and ergodic measures andprovide examples of economic applications. The question ofattractiveness and observability, already considered in Part I, isrevisited and the concept of natural, or physical, measure isexplained. This theoretical apparatus then is applied to the questionof predictability of dynamical systems, and the notion of metricentropy is discussed. Finally, we consider the class of Bernoullidynamical systems and discuss the possibility of distinguishingorbits of deterministic chaotic systems and realizations ofstochastic processes.

INVARIANT PROBABILITY DISTRIBUTIONS IN ECONOMIC MODELS: A GENERAL RESULT

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.

NONLINEAR DYNAMICS AND CHAOS PART I: A GEOMETRICAL APPROACH

This paper is the first part of a two-part survey reviewing somebasic concepts and methods of the modern theory of dynamical systems.The survey is introduced by a preliminary discussion of the relevanceof nonlinear dynamics and chaos for economics. We then discuss thedynamic behavior of nonlinear systems of difference and differentialequations such as those commonly employed in the analysis ofeconomically motivated models. Part I of the survey focuses on thegeometrical properties of orbits. In particular, we discuss thenotion of attractor and the different types of attractors generatedby discrete- and continuous-time dynamical systems, such as fixed andperiodic points, limit cycles, quasiperiodic and chaotic attractors.The notions of (noninteger) fractal dimension and Lyapunovcharacteristic exponent also are explained, as well as the mainroutes to chaos.