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Improved Estimates of Survival Probabilities via Isospectral Transformations

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Book cover Ergodic Theory, Open Dynamics, and Coherent Structures

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 70))

Abstract

We consider open systems generated from one-dimensional maps that admit a finite Markov partition and use the recently developed theory of isospectral graph transformations to estimate a system’s survival probabilities. We show that these estimates are better than those obtained through a more direct approach.

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References

  1. Afraimovich, V.S., Bunimovich, L.A.: Which hole is leaking the most: A topological approach to study open systems. Nonlinearity 23, 644–657 (2010)

    Article  MathSciNet  Google Scholar 

  2. Afraimovich, V., Bunimovich, L.: Dynamical networks: Interplay of topology, interactions, and local dynamics. Nonlinearity 20, 1761–1771 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bakhtin, Y., Bunimovich, L.A.: The optimal sink and the best source in a Markov chain. J. Stat. Phys. 143, 943–954 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  4. Blank, M.L., Bunimovich, L.A.: Long range action in networks of chaotic elements. Nonlinearity 19, 330–345 (2006)

    Article  MathSciNet  Google Scholar 

  5. Bunimovich, L.A.: Fair dice-like hyperbolic systems. Contemp. Math. 467, 79–87 (2012)

    Article  MathSciNet  Google Scholar 

  6. Bunimovich, L.A., Webb, B.Z.: Isospectral graph transformations, spectral equivalence, and global stability of dynamical networks. Nonlinearity 25, 211–254 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bunimovich, L.A., Webb, B.Z.: Dynamical networks, isospectral graph reductions, and improved estimates of Matrices’ spectra. Linear Algebra Appl. 437(7), 1429–1457 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bunimovich, L.A., Yurchenko, A.: Where to place a hole to achieve the fastest escape rate. Israel J. Math. 182, 229–252 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Demers, M., Wright, P.: Behavior of the escape rate function in hyperbolic dynamical systems. Nonlinearity 25, 2133–2150 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Varga, R.: Gershgorin and His Circles. Springer, Berlin (2004)

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. ABC Math Program and School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332, USA

    L. A. Bunimovich

  2. Laboratory of Statistical Physics, Rockefeller University, 1230 York Avenue, New York, NY, 10065, USA

    B. Z. Webb

Authors
  1. L. A. Bunimovich
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  2. B. Z. Webb
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Corresponding author

Correspondence to L. A. Bunimovich .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Leicestershire, Leicestershire, United Kingdom

    Wael Bahsoun

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    Christopher Bose

  3. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Gary Froyland

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Bunimovich, L.A., Webb, B.Z. (2014). Improved Estimates of Survival Probabilities via Isospectral Transformations. In: Bahsoun, W., Bose, C., Froyland, G. (eds) Ergodic Theory, Open Dynamics, and Coherent Structures. Springer Proceedings in Mathematics & Statistics, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0419-8_7

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