RALPH ABRAHAM Professor Emeritus of Mathematics B.S.E. Engineering, M.S. Mathematics, Ph.D. Mathematics: University of Michigan My Page

Phone: 831-459-3158 Office: Baskin 179 Office Hours: By Appt. Email: abraham_at_vismath_dot_org

RESEARCH INTERESTS

Ralph Abraham's work is devoted to applied and computational Mathematics.  His focus is on the theories of dynamical systems, chaos and bifurcations.  His applications span the Physical, Biological, and Social sciences, and the history of Mathematics.

SELECTED PUBLICATIONS

Books:

R. Abraham, J. Marsden: The Foundations of Mechanics, Benjamin Press, 1967, Addison-Wesley, 1978.

R. Abraham, J. Robbin: Transversal Mappings and Flows, Benjamin Press, 1967.

R. Abraham: Linear and Multilinear Algebra, Benjamin Press, 1967.

R. Abraham, J. Marsden, T. Ratiu: Manifolds, Tensor Analysis, and Applications, Addison Wesley, 1983, Springer-Verlag, 1988.

R. Abraham, C. Shaw: Dynamics, the Geometry of Behavior, Aerial Press, 1982-1988, Addison Wesley, 1992.

R. Abraham, T. McKenna, R. Sheldrake: Trialogues at the Edge of the West, 1992, reprinted as Chaos, Creativity, and Cosmic Conciousness, Park Street Press, 2001.

R. Abraham: Chaos, Gaia, Eros, Harper San Francisco, 1994.

R. Abraham, F. Jas, W. Russell: The Web Empowerment Book, Springer, 1995.

R. Abraham, L. Gardini, C. Mira: Chaos in Discrete Dynamical Systems, Springer, 1997.

R. Abraham, T. McKenna, R. Sheldrake: The Evolutionary Mind: Trialogues at the Edge of the Unthinkable, Dakota Books, 1997.

R. Abraham, Y, Ueda: The Chaos Avant-Garde, World Scientific Publishing Co., 2001.

R. Abraham: Bolts from the Blue, to appear 2005.

Papers:

R. Abraham, A. Garfinkel: The Dynamics of Synchronization and Phase Regulation, 2003.

R. Abraham, Y. Ueda, M. Hirano, H. Ohta: Attractor and Basin Portraits of a Double Swing Power System, IJBC 14(9), Sept. 2004, 3135-3152.

R. Abraham, Y. Ueda, H. Ohta: Basic Sets and Attractors of a Double Swing Power System, to appear, 2004.

R. Abraham, D. Friedman: Landscape Dynamics and Conspicuous Consumption, To appear, Proceedings of Intern. Symposium on Dynamic Games and Applications, Tucson, Dec. 2004.

R. Abraham, D. Friedman: Landscape Dynamics, Complex Dynamics, and Agent Based Models, Submitted to Nonlinear Dynamics in Psychology and the Life Sciences, 2005.

PERSONAL WEBPAGE:

http://www.ralph-abraham.org/

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