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Semigroups, Attractors, and Products of Random Matrices

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Probability Measures on Groups X

Abstract

In this paper we define attractors in a natural manner and then use semigroup ideas to find a convenient formula for their determination. Recurrent random walks in matrices will appear in our discussions and be part of the total picture. We will use our formula to determine completely two interesting attractors. one a well-known Sierpinsky gasket and the other an unbounded version of the gasket.

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References

  1. Barnsley, M.F. S G. Demko, J.H. Elton, and J. SGeronimo (1988), Invariant measures for Markov processes arising from iterated function systems with place dependent probabilities. Ann. Inst. Henri Poincare 24, No. 3, 367–394

    MathSciNet  MATH  Google Scholar 

  2. Elton, J.H. (1987). An ergodic theorem for iterated maps. Ergod. Th & Dynam. Sys 7, 481–488

    Article  MathSciNet  MATH  Google Scholar 

  3. Furstenberg, H. and Y. Kifer (1983). Random matrix products and measures on projective spaces. Israel J. Math. 46, 12–32.

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  4. Hutchinson, J.E. (1981). Fractals and self-similarity. Indiana University Math J. 30, 713–747

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  5. Mukherjea, A. (1991). Recurrent random walks in nonnegative matrices: attractors of certain iterated function systems. Prob. Th & Rel. Fields (accepted for publication).

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  6. Mukherjea, A. and N.A. Tserpes (1976). Measures on Topological Semigroups: Convolution products and Random Walks. Springer LNM 547.

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Author information

Authors and Affiliations

  1. University of South Florida, Tampa, Florida, 33620-5700, USA

    Arunava Mukherjea

Authors
  1. Arunava Mukherjea
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Editor information

Editors and Affiliations

  1. University of Tübingen, Tübingen, Germany

    Herbert Heyer

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© 1991 Springer Science+Business Media New York

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Mukherjea, A. (1991). Semigroups, Attractors, and Products of Random Matrices. In: Heyer, H. (eds) Probability Measures on Groups X. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2364-6_23

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  • DOI: https://doi.org/10.1007/978-1-4899-2364-6_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-2366-0

  • Online ISBN: 978-1-4899-2364-6

  • eBook Packages: Springer Book Archive

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