Papers

• Christopher Bose & Rua Murray. Polynomial decay of correlations in the generalized baker's map. Submitted (366 kB PDF)
• Christopher Bose & Rua Murray. Estimating risk-neutral probability measures via MAXENT. Submitted (230 kB PDF)
• 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 and 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) (262kB PDF)
• 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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Last modified: August 3, 2010.