# WMI Preprints 1985

*Furstenberg's theorem for nonlinear stochastic systems,*

by A.P. Carverhill

*Lyapunov exponents for a stochastic analogue of the geodesic flow,*

by A.P. Carverhill & K.D. Elworthy

*Harmonic maps and minimal surface coboundaries,*

by K.-C. Chang & J. Eells

*Birational pairs according to S. Iitaka,*

by D. Dicks

*The C*-algebras of the two-dimensional Ising model,*

by D.E. Evans

*The global homological dimension of the ring of differential operators on a non-singular variety over a field of positive characteristic,*

by S.P. Smith

*Normal forms for singularities of the tangent developable of a space curve,*

by D. Mond

*Relative pressure, relative equilibrium states, compensation functions and many-to-one codes between subshifts,*

by P. Walters

*Unique ergodicity and random matrix products,*

by P. Walters

*Derivations tangential to compact groups: the nonabelian case,*

by O. Bratteli & D.E. Evans

*Survey: Lyapunov exponents for stochastic flows on manifolds,*

by A.P. Carverhill

*Unstable minimal surface coboundaries,*

by K.-C. Chang & J. Eells

*Bounds for average Lyapunov exponents of gradient stochastic systems,*

by M.J. Chappell

*Hyperbolic structure preserving isomorphisms of Markov shifts,*

by K. Schmidt

*On a C*-algebra approach to phase transition in the two-dimensional Ising model. II,*

by D.E. Evans & J.T. Lewis

*Lectures on orbits of minimal action for area-preserving maps,*

by S. MacKay & J. Stark

*C*-algebras associated with Denjoy homeomorphisms of the circle,*

by I. Putnam, K. Schmidt & C. Skau

*The extraordinary derived cateogory,*

by C.A. Robinson

*The problem of "global colour" in gauge theories,*

by P.A. Horváthy & J.H. Rawnsley

*James-Hopf invariants and the Hilton-Milnor theorem,*

by B.J. Sanderson

*Differential operators on commutative algebras,*

by S.P. Smith

*A twistorial characterization of conformal branched immersions with parallel mean curvature,*

by M.J. Ferreira

*Cyclic homology and equivariant homology,*

by J.D.S. Jones

Twistor methods,

by J. Rawnsley

*The Hurwitz constant and diophantine approximation on Hecke groups,*

by A. Haas & C. Series

*Geometrical Markov coding of geodesics on surfaces of constant negative curvature,*

by C. Series

*Noetherian rings whose factor rings are orders in Artinian rings,*

by E.P. Armendariz & C.R. Hajarnavis

*Algebraic linearity for an automorphism of a surface,*

by J.S. Birman & C. Series

*A formula for the Lyapunov numbers of a stochastic flow application to a perturbation theorem,*

by A. Carverhill

*Synchronisation of canonical measures for hyperbolic attractors,*

by W. Parry

*Undergraduate algebraic geometry,*

by M. Reid

*Differential operators on an affine curve,*

by S.P. Smith & J.T. Stafford

*On the energy spectrum of harmonic 2-spheres in unitary groups,*

by G. Valli

*Harmonic spheres in compact Lie groups and holomorphic curves in homogeneous spaces,*

by F. Burstall & J. Rawnsley

*T-points: a codimension two heteroclinic bifurcation,*

by P. Glendenning & C. Sparrow

*Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators,*

by M. Golubitsky & I. Stewart

*Flux and differences in action for continuous time Hamiltonian systems,*

by R.S. MacKay & J.D. Meiss

*A characterisation of homotopy 3-spheres: I,*

by E. Rego & C. Rourke

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