Title | A FAMILY OF RANDOM MAPS WHICH POSSES INFINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURES |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | ISLAM SHAFIQUL |

Journal | Dynamic Systems and Applications |

Volume | 27 |

Issue | 4 |

Start Page | 729 |

Pagination | 14 |

Date Published | 09/2018 |

ISSN | 1056-2176 |

AMS Subject Classification | 37A05, 37H10 |

Abstract | We consider a family of random maps where each of the component maps is from a family of piecewise, linear and Markov maps on a class of infinite partitions of the state space. We investigate the existence of infinite absolutely continuous invariant measures of the random maps. In a more general setting, our study establishes a positive answer to the question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? This question is analogous to Parrondo’s paradox [5] which states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. |

https://acadsol.eu/dsa/articles/27/4/3.pdf | |

DOI | 10.12732/dsa.v27i4.3 |

Refereed Designation | Refereed |

Full Text | ## REFERENCES[1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs, American Mathematical Society, 1997. |