Fractal attractors and singular invariant measures in two-sector growth models with random factor shares
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Date
2018-05-01
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Communications in Nonlinear Science and Numerical Simulation
Abstract
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.
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Keywords
Two-sector growth model, Stochastic factor shares, Fractal attractors, Singular measures
Citation
Davide La Torre, Simone Marsiglio, Franklin Mendivil, Fabio Privileggi, Fractal attractors and singular invariant measures in two-sector growth models with random factor shares, In Communications in Nonlinear Science and Numerical Simulation, Volume 58, 2018, Pages 185-201