caa a22 4500 445361271 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s11071-010-9891-3 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9891-3 Dynamics on certain sets of stochastic matrices [Elektronische Daten] [C. CorreiaRamos, Nuno Martins, A. NascimentoBaptista] We study iteration of polynomials on symmetric stochastic matrices. In particular, we focus on a certain one-parameter family of quadratic maps which exhibits chaotic behavior for a wide range of the parameters. The well-known dynamical behavior of the quadratic family on the interval, and its dependence on the parameter, is reproduced on the spectrum of the stochastic matrices. For certain subclasses of stochastic matrices the referred dynamical behavior is also obtained in the matrix entries. Since a stochastic matrix characterizes a Markov chain, we obtain a discrete dynamical system on the space of reversible Markov chains. Therefore, depending on the parameter, there are initial conditions for which the corresponding reversible Markov chains will lead under iteration to a fixed point, to a periodic point, or to an aperiodic point. Moreover, there are sensitivity to initial conditions and the coexistence of infinite repulsive periodic orbits, both features of chaos. Springer Science+Business Media B.V., 2010 Matrix dynamics nationallicence Stochastic matrices nationallicence Iterated interval maps nationallicence Reversible Markov chains nationallicence CorreiaRamos C. Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal aut Martins Nuno Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal aut NascimentoBaptista A. CIMA, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal aut Nonlinear Dynamics Springer Netherlands 65/3(2011-08-01), 301-310 0924-090X 65:3<301 2011 65 11071 https://doi.org/10.1007/s11071-010-9891-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9891-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- CorreiaRamos C. Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal aut NATIONALLICENCE 700 1- Martins Nuno Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal aut NATIONALLICENCE 700 1- NascimentoBaptista A. CIMA, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/3(2011-08-01), 301-310 0924-090X 65:3<301 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer