BA Mathematics - **Oxford** 1968

Ph.D Theoretical Chemistry - **Wisconsin** 1972

Research, **Centre Etudes Nucleaires de Saclay (Paris) **1977-1979

Professor, President's Advisory Committee, **Georgia Institute of Technology** 1979-1991

Adjunct Professor, **Center for Dynamical Systems, Georgia Institute of Technology** 1999-2000

Adjunct Professor, Mathematics, **University of New South Wales** 1995-1999

Miegunyah Distinguished Fellow, **University of Melbourne** 1998

Honorary Professorial Fellow **University of Melbourne** 1999-2002

Organizer of special year (2000-2001) at the Institute of Mathematics and Applications (Minnesota)

Organiser of a conference on Fractals in Multimedia for January 2001.

Visiting Fellow, Mathematics, **Australian National University** Sep-Nov 2002

Professor, Mathematics, **Australian National University** 2004 - present

"Sum rule Functions," J. Math Phys. (1971) 12, 958-964.

"The bounding properties of the multipoint Padé approximant to a series
of Stieltjes on the real line," J. Math. Phys. (1973) 14, 299-313.

"A variational approach to the theory of multipoint Padé approximants,"
(with S. T. Epstein) J. Math. Phys. (1973) 14, 314-325.

"Dual variational principles and Padé type approximants," (with P. D.
Robinson) J. Inst. Maths and Applics. (1974) 14, 229-249.

"Padé-approximant bounds and approximate solutions for Kirkwood-Riseman
Integral Equations" (with P. D. Robinson) J. Inst. Maths and Applics.
14 (1974), 251-265.

"Bivariational bounds," (with P. D. Robinson) Proc. Roy. Soc. London (1974) A338, 527-533.

"Variational bounds on overlaps," (with P. D. Robinson) J. Phys. A (1975) 8, 654-663.

"New variational bounds on expectation values," (with P. D. Robinson) J. Phys. A (1975) 8, 195-198.

"Variational bounds on transition probabilities," (with P. D. Robinson) Internatl. J. of Quantum Chem. (1975) 9, 479-487.

"Bounds on dynamical polarizabilities at high frequencies," Mol. Phys. (1975) 29, 1377-1386.

"Pointwise bounds for eigenfunctions of one-electron systems," Phys. Lett. (1975) 53A, 123-126.

"Correction terms for Padé approximants," J. Math. Phys. (1975) 16, 918-928.

"Padé approximant bounds for the difference of two series of Stieltjes," J.Math. Phys. (1975) 17, 559-565.

“Bivariational bounds in a complex Hilbert space, and correction terms
for Padé approximants," (with G. A. Baker, Jr.) J.Math. Phys. (1976)
17, 1019-1027.

"Bivariational bounds associated with non-self-adjoint linear
operators," (with P. D. Robinson) Proc. Roy. Soc. Edin. (1976) 75A,
109-118.

"Bivariational bounds on solutions of two-point boundary value
problems," (P. D. Robinson) J. Math. Anal. Applics. (1976) 56, 172-184.

"Bivariational bounds for non-linear problems," (1977) J. Inst. Maths. Applics. 20, 485-504.

"Propriétes d'analyticité et de positivité de la solution positive
d'une class d'equations elliptiques non linéaires," (with D.
Bessis)(1977), C. R. Acad. Sc. Paris, t. 285, series A, 233-235.

"Lower bounds for quantum mechanical energy levels," (1977) J. Phys. A. 11, 55-68.

"Pointwise bivariational bounds on solutions of Fredholm integral
equations," (with P. D. Robinson) (1977), SIAM J. Math. Anal. 16,
135-144.

"Rational approximant bounds for a class of two-variable Stieltjes functions," (1978) SIAM J. Math. Anal. 9, 272-290.

"Padé approximant bounds on the positive solutions of some non-linear
elliptic equations," (with D. Bessis) (1978) Proc. R. Soc. Edin., 80A,
183-200.

"On the approximation of potential energy functions for diatomic
molecules," (with J. Aguilar) (1978), Int. J. Quant. Chem. 13 (1978)
642-677.

"The Diophantine moment problem and the analytic structure in the
activity of the ferromagnetic Ising model," (with D. Bessis and P.
Moussa) (1979) J. Math. Phys. 20, 535-545.

"Constructive methods based on analytic characterizations and their
application to non-linear elliptic and parabolic differential
equations," (1979) (with D. Bessis) J. Math. Phys. 20, 1135-1145.

"Rigorous bounds on charge densities from form factor data," (with G. Turchetti) Phys. Rev. C (1979) 20, 1175-1185.

"On the Abel transformation and the nonlinear Boltzmann equation," (with G. Turchetti) Phys. Lett. (1979) 72A, 417-419.

"Generalized Padé resummation of a nonlinear Boltzmann equation," (with G. Turchetti) Nuovo Cimento Lett. (1979) 26, 188-192.

"On a class of solutions of the Krook-Tjon-Wu Model of the Boltzmann
equation," (with H. Cornille) J. Math Phys. 21 (1980), 1176-1193.

"Bounds for all characteristic frequencies of beaded strings and
electrical filters," (with R. Duffin) Proc. Nat. Acad. Sci. 77 (1980)
3120-3124.

"General solution of a Boltzmann equation and the formation of
Maxwellian tails," (with H. Cornille), Proceedings of the Royal Society
of London A374 (1981), 371-400.

"Bounding methods in nuclear physics" (with G. Turchetti) Computer Physics Communications 22 (1981) 325-343.

"Some operators which commute in a nonlinear Boltzmann equation" (with
J. Herod, D. Mosher, G. Passty) Nuovo Cimento Letters, 32 (1981)
437-442.

"Nonlinear Boltzmann equations and kinetic stochastic equations" Nuovo Cimento Letters 30 (1981), 339-362.

The calculation of some solutions of the Bobylev-Krook-Wu and Tjon-Wu
equations" (with G. Turchetti), Nuovo Cimento 65B (1981), 1-25.

"The Tjon-Wu equation in Banach space settings" (with V. Jory, J.
Herod, G. Passty) Journal of Func. Analysis 43 (1981), 32-51.

"Projection method for Boltzmann energy equations" (with G. Turchetti), Nuovo Cimento Letters 33 (1982), 347-351.

"Orthogonal polynomials associated with invariant measures on Julia
Sets," (with J. S. Geronimo, A. N. Harrington) Bulletin A.M.S. 7
(1982), 381-384.

"On the invariant sets of a family of quadratic maps," (with J. S.
Geronimo and A. N. Harrington), Comm. Math. Phys. 88 (1983), 479-501.

"Infinite dimensional Jacobi matrices associated with Julia sets,"
(with J. S. Geronimo and A. N. Harrington), Proc. A.M.S. 88 (1983),
625-630.

"Some tree-like Julia sets and Padé approximants," (with J. S.Geronimo
and A. N. Harrington), Letters in Math. Phys. 7 (1983), 279-286.

"Solutions for a model Boltzmann equation by monotonicity methods"
(with J. Herod, D. Mosher, G. B. Passty) Houston Journal of Mathematics
9 (1983), 345-356.

"A study of Boltzmann energy equations" (with G. Turchetti) Annals of Physics 159 (1985), 1-61.

"Moments of balanced measures on Julia sets" Trans. Am. Math. Soc. 284 (1984), 271-280.

"Geometry and combinatorics of Julia sets of real quadratic maps" (with
J. S. Geronimo, A. N. Harrington) J. Stat. Phys. 37 (1984), 51-92.

"Geometry, electrostatic measure, and orthogonal polynomials on Julia
sets for polynomials" (with J. S. Geronimo and A. N. Harrington),
Journal of Ergodic Theory and Dynamical Systems 3 (1983), 509-520.

"Condensed Julia sets, with an application to a fractal lattice model
Hamiltonian" (with J. S. Geronimo, A. N. Harrington) Trans. A.M.S. 288
(1985), 537-561.

"A Mandelbrot set for pairs of linear maps" (with A. N. Harrington) J. Physica 15D (1985), 421-432.

"Almost-periodic Jacobi matrices associated with Julia sets for
polynomials" (with J. S. Geronimo, A. N. Harrington) Comm. Math. Phys.
99 (1985) 303-317.

"Iterated function systems and the global construction of fractals"
(with S. G. Demko) Proceedings of the Royal Society of London 399
(1985), 243-275.

"Iterated networks and the spectra of renormalizableelectromechanical
systems" (with T. D. Morley, E. R. Vrscay) Journal of Statistical
Physics 40 (1985), 39-67.

"Solution of an inverse problem for some strange attractors and other
fractals" (with V. Ervin, D. Hardin, J. Lancaster) Proceedings of the
National Academy of Sciences 83 (1986) 1975-1977.

"Fractal functions and interpolation", Constructive Approximation, 2(1986), 303-329.

"A New Class of Markov Processes for Image Encoding" (with J. Elton), Advances in Applied Probability 20, (1988)14-32.

Fractals Everywhere, a textbook and research monograph devoted to
detrministic fractal geometry. (September 1988), Academic Press/
Harcourt-Brace-Jovanovitch.

Fractal Approximation Theory, a special issue of the Journal of
Constructive Approximation, edited by Michael F. Barnsley, published by
Springer-Verlag Vol.5, No.1, 1989.

The Science of Fractal Images, ( with R. Devaney, B. Mandelbrot, H.
Peitgen, D. Saupe, and R. Voss), a book published by Springer-Verlag
(September 1988).

"The Calculus of Fractal Interpolation Functions" (with A. N. Harrington), Journal of Approximation Theory, 57 (1989),14-34.

"Recurrent Iterated Function Systems" (with J. Elton, D. Hardin), Journal of Constructive Approximation, 5(1989), 3-31.

"Harnessing Chaos for Image Synthesis" (with L. Reuter, A. Jacquin, F.
Malassenet, and A. Sloan), Computer Graphics 22 (1988), 131-140

"Hidden Variable Fractal Interpolation Functions" ( with P. Massopust,
J.Elton, D.Hardin), SIAM Journal on Mathematical Analysis, 20 (1989),
1218-1233.

"Mixing Markov Chains and Their Images", ( Marc Berger and Mete Soner)
Probability for the Engineering and Information Sciences, 2, (1988),
387-414.

"A Mandelbrot Set whose Boundary is Piecewise Smooth" (with D. Hardin), Trans. Am. Math. Soc. (1989)

"Image Compression by Simulated Thermal Annealing" (with A. Sloan) Journal of Applied and Computational Mathematics.

"An Open Mapping Theorem and its Applications to Image Computation."( with G. Cain, R. Kasriel, and J. Herndon).

"Local Contractions and Recurrent Iterated Function Systems." ( with G.
Cain, A. Jacquin, and R. Kasriel) - submitted for publication to the
Journal of the London Mathematical Society September 1989.

"Multifunction Dynamics." ( with G. Cain, Robert Kasriel) - 1990.

Fractal Image Compression (with L. P. Hurd) a book describing the
mathematics of fractal image compression and the fractal transform
process published by AK Peters, Wellesley, MA., 1993

Fractals Everywhere - Second Edition. A revised version of the 1988
publication with additional material on recurrent Iterated Function
Systems published by Academic Press, August 1993.

"The bounding properties of the multipoint Padé -approximant," Rocky Mtn. J. of Math. 4 (1974), 331-333.

"Bivariational bounds on (x,g), when Ax = f," (with P. D. Robinson),
Lecture Notes in Mathematics (Springer Verlag, Berlin), 415 (1974),
308-310.

"Bivariational bounds on (x,f), for nonlinear problems Fx = 0", (with
P. D. Robinson), Lecture Notes in Mathematics, (Springer-Verlag,
Berlin), 564 (1976), 26-33.

"Approximants for some classes of multivariable functions provided by
variational principles," in Multivariate Approximation, D. C. Handscomb
Editor, Academic (1978), 95-104.

"Parameters dependences of solutions of classes of quasilinear elliptic
and parabolic differential equations," in Bifurcation and Nonlinear
Eigenvalue Problems, Lecture Notes in Mathematics (Springer Verlag,
Berlin) 782 (1979), 1-15.

"New results on the nonlinear Boltzmann equation" (with G. Turchetti)
in Bifurcation Phenomena in Mathematical Physics and Related Topics,
edited by C. Bardos and D. Bessis, Reidel Publishing Company (1980),
351-370.

"Analysis of Boltzmann equations in Hilbert space by means of a
nonlinear eigenvalue property" (with J. Herod, D. Mosher, G. Passty) in
Spectral Theory of Differential Operators, edited by I. W. Knowles and
R. T. Lewis, North-Holland (1981), 45-52.

"Bounds for the linearly perturbed eigenvalue problem," in
SpectralTheory of Differential Operators, edited by I. W. Knowles and
R. T. Lewis, North-Holland (1981), 37-43.

"Approximation theory on a snowflake" (with J. S. Geronimo, A. N.
Harrington, and L. D. Drager) in Multivariate Approximation Theory,
Vol. II, edited by W. Schempp and K. Zeller,Birkhauser (1982), 37-41.

"Julia sets and autonomous differential equations" (with A. N.
Harrington) in Differential Equations, I. W. Knowles and R. T. Lewis
(Editors), North Holland 1984, 37-41.

"Geometrical and electrical properties of some Julia sets" (with A. N.
Harrington, J. S. Geronimo) in Classical and quantum models and
arithmetic problems, D. V. Chudnovsky and G. V. Chudnovsky (Editors),
Dekker 1984, 1-68.

"Chaos in electro-mechanical sytems and fractals" (with T. D. Morley)
in Proceedings of Southeastern Conference on Theoretical and Applied
Mechanics XIII (1984).

"Rational approximation of fractals" (with S. G. Demko) Springer-Verlag
Lecture Notes in Mathematics, edited by E. B. Saff and P. R. Graves
Morris (1984).

"Estimates and bounds for the doubly perturbed eigenvalue problem"
(with W. Raddatz) in Multivariate Approximation Theory, Vol. II, edited
by W. Schempp and K. Zeller, Birkhauser (1982), 43-45.

"Constructing fractal objects with Iterated Function Systems" (with S.
Demko, L. Hodges, B. Naylor) SIGRAPH 19 (1985), 271-278.

Editor with S. Demko of Chaotic Dynamics and Fractals, a conference proceedings, published by Academic Press, Fall 1985.

"Making chaotic dynamical systems to order," in Chaotic Dynamics and
Fractals, edited by M. Barnsley, and S. Demko, Academic, 1985.

"Fractal Modelling of Biological Structures," (with P. Massopust, H.
Strickland, A. D. Sloan) Annals of the New York Academy of Sciences,
504 (1987), 179-194.

"Fractal Image Encoding," (with J. H. Elton, A. D. Sloan, H.
Strickland), Unconventional Photoactive Solids, Edited by H. Sher,
Plenum 1988, 1-11.

"Two lectures on fractal geometry," E coles CEA-EDF-INRIA 1986, INRIA Rocquencourt, France, pp. 95-115.

"Chaos in Computer Graphics", (with Alan D. Sloan), Computer Graphics World, November 1987.

"A Better Way to Compress Images" (with Alan D. Sloan), Byte Magazine 13(1988), 215-223.

"Fractal Modelling of Real World Images", in Fractals: Introduction, Basics, and Perspectives ,
published by SIGGRAPH, Course Notes #15, published July 1987, sponsored by ACM.

"Pictures Worth a Million Words" (with Marc A. Berger) in Projects in
Scientific Computing 1988-89, published by Pittsburgh Supercomputing
Center.