Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

Authors

Davide La Torre, Nazarbayev University, University of Milan
Simone Marsiglio, University of WollongongFollow
Franklin Mendivil, Acadia University
Fabio Privileggi, University of Turin

RIS ID

115548

Publication Details

La Torre, D., Marsiglio, S., Mendivil, F. & Privileggi, F. (2018). Fractal attractors and singular invariant measures in two-sector growth models with random factor shares. Commun Nonlinear Sci Numer Simulat, 58 185-201.

Abstract

We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley's fern attractor.