Office hours
- Tues 11.00-12.30 (Ersk415)
Research
Teaching
Misc
> Rua's homepage
Research interests
- Dynamical systems
- Ergodic theory
- Maximum entropy optimisation methods, applied primarily to dynamical systems
- Numerical effects in dynamics
Publications
Preprints
- Christopher Bose, Cecilia Gonzalez-Tokman, Gary Froyland & Rua Murray. Ulam'S method for Lasota-Yorke maps with holes. Preprint on arXiv. Submitted
- Christopher Bose & Rua Murray. Maximum entropy estimates for
risk-neutral probability measures with non-strictly-convex
data. Submitted (332 kB PDF)
Papers
- Gary Froyland, Rua Murray & Ognjen Stancevic. Spectral degeneracy and
escape dynamics for intermittent maps with a hole. Nonlinearity 24 (2011) 2435-2463. http://dx.doi.org/10.1088/0951-7715/24/9/003.doi. Preprint: http://arxiv.org/abs/1012.2149
- Rua Murray. Ulam's method for some non-uniformly expanding maps. Discrete and continuous dynamical systems. 26(3):1007-1018 (2010). Preprint (302 kB PDF)
- Gary Froyland, Rua Murray & Dalia Terhesiu. Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Phys. Rev. E 76 (2007) 036702
- Christopher J. Bose & Rua Murray. Duality and the computation of approximately invariant measures for non-singular transformations. SIAM J. Optimization 18(2):691-709 (2007) Preprint (327kB PDF)
- Mirela Domijan, Rua Murray & James Sneyd. Dynamical probing of the mechanisms underlying calcium oscillations. J. Nonlinear Science. 16(5):483-506 (2006).
- Christopher J. Bose & Rua Murray. Dynamical conditions for convergence of a maximum entropy method for Frobenius-Perron operator equations. Appl. Math. Comp. 182(1):210-212 (2006).
- Christopher J. Bose & Rua Murray. Minimum 'energy' approximations to invariant measures for nonsingular transformations.Discrete and Continuous Dynamical Systems, 14(3):597-615 (2006).
- Rua Murray. Optimal partition choice for invariant measure approximation for one-dimensional maps. Nonlinearity 17(5):1623-1644 (2004).
- Giovanni Santoboni, Rua Murray & Steven Bishop. A simple use of the diffusion approximation for treating roundoff-induced problems in coupled maps with an invariant subset. Space-time chaos (Pamplona, 2000), 223--232, World Sci. Publishing, River Edge, NJ. (2001)
- Christopher J. Bose & Rua Murray. The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems, 7(1):219-235 (2001).
- Giovanni Santoboni, Rua Murray & Steven Bishop. Round-off induced phenomena and diffusion processes: the 'premature' synchronisation of coupled maps. Phys. Lett. A, 271:358-367 (2000).
- Rua Murray. Existence, mixing and approximation of invariant densities for expanding maps on R r. Nonlinear Analysis TMA, 45(1):37-72 (2001). Preprint (362Kb PDF).
- Rua Murray. Approximation error for invariant density calculations. Discrete & Continuous Dynamical Systems, 4(3):535-557 (1998).
- M Keane, R Murray & L-S Young. Computing invariant measures for expanding circle maps. Nonlinearity, 11:27-46 (1998). Preprint version (331Kb PDF)
- R Murray. Invariant measures and stochastic discretisations of dynamical systems. Proceedings of 15th IMACS World Congress, Berlin, 1997. (144Kb PDF)
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).
> Rua's homepage
