2002/07/31 by David Romero, Federico Zertuche · 2 citations
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #physics.bio-ph #physics.gen-ph
paper · pdf · doi:10.1088/0305-4470/36/13/304
16 pages, 1 figure. Minor changes. To be published in Journal of Physics A: Mathematical and General
arxiv created 2003/03/15 · openalex publication_date 2003/03/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as its image. We derive here explicit formulae for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulae increases exponentially with n ; therefore, they are not directly applicable to study the behaviour of systems where n is large. However, our formulae can be used to derive useful asymptotic expressions, as we show.