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Research interests

  • Dynamical systems and ergodic theory
  • Maximum entropy optimisation methods
  • Numerical effects in dynamics
  • Mathematical physiology
My core research is in the general area of dynamical systems. The subject is exciting because it is a meeting place for real applications, numerical computation and beautiful theorems. A lot of my work is on the probabilistic side of dynamical systems: this is called "ergodic theory", where one seeks to know about the statistical properties of complex systems. I have made significant contributions in "numerical ergodic theory": approximation of important dynamical objects on a computer, with confidence in the accuracy of the output, backed by mathematical rigour. Since joining the University of Canterbury I have worked with collaborators on applications in ecology, energy, finance and physiology.

Publications

Preprints

  • Christoper Bose & Rua Murray. First hyperbolic times for intermittent maps with unbounded derivative. Preprint on arXiv.To appear in Dynamical systems: an international journal (2014)
  • Christopher Bose, Cecilia Gonzalez-Tokman, Gary Froyland & Rua Murray. Ulam's method for Lasota-Yorke maps with holes. Preprint on arXiv. To appear in SIAM Journal on Applied Dynamical Systems (2014)
  • Christopher Bose & Rua Murray. Numerical approximation of conditionally invariant measures via Maximum Entropy. Preprint on arXiv. To appear in edited book: Ergodic theory, open dynamics, and coherent structures. Springer Proceedings in Mathematics & Statistics. Volume 70. ISBN 978-1-4939-0418-1

Papers

Other

  • Rua Murray. Approximation of invariant measures for a class of maps with indifferent fixed points. University of Waikato, Mathematics Research Report Series II No. 106. (2005)
  • Christopher J Bose & Rua Murray. Variational methods for the approximation of invariant measures. University of Waikato, Mathematics Research Report Series II No. 100. (2004)
  • Rua Murray. Discrete approximation of invariant densities (2.6Mb PDF). PhD Thesis. University of Cambridge, August 1997.
  • Rua Murray, Approximation error for invariant density calculations. Statistical Laboratory Research Report 1997-10 (1997).
  • R D A Murray. Approximation and concrete error bounds for ACIM density approximation for C 1+α expanding mappings.Statistical Laboratory Research Report 1996-22 (1996).
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