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1864 Steriade, M., McCarley, R.W. (1990) Brainstem Control of Wakefulness and Sleep. Plenum. N.Y. 289 HOUSE_OVERSIGHT_013789 Stillwell, J. (1985) Poincare’s Papers on Fuchsian Groups. Springer-Verlag, N.Y. pp 1-50 Stockbridge,L.L., French,A.S. (1989) Characterization of a calcium-activated potassium ch
ormly divergent (and convergent), “hyperbolic” chaotic systems, such as brain systems, behave in Euclidean space, an intuitive similarity about which Poincare experienced his famous vacation bus trip epiphany (Stillwell, 1985). It should also be noted that encoding neural spike trains in one dimension for s
17:1179-1196 Cooper, N.G. (1987): From Cardinals to Chaos, Cambridge University Press, Cambridge. Cornfield, |.P., Fomin, S.V., Sinai, Ya.G. (1982) Ergodic Theory. Springer-Verlag. Berlin Crevier,D.W., Meister,M (1998): Synchronous period-doubling in flicker vision of salamander and man. J Neurophysiol. 79:18
context of mathematical epistemology, the instantaneous images of a geometer contrast with the labored sequential logic of the mathematical analyst. Poincare’ claimed that inclinations toward one or the other of these two cognitive styles and their associated mathematical tools arise from different kinds o
g 7:809-888, 1986. Thermodynamics, Enrico Fermi, Dover, N.Y. 1956. Thermodynamics and Statistical Mechanics, Peter T. Landsberg, Dover, N.Y. 1978. Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, T. Bedford, M. Keane and C. Series, Oxford, Oxford, 1991. The Mathematical Theory of Communication, Claude
blished a model of it through internal reconstructions of sequential sensory experiences that_accompanied our exploratory movements. A world. It was Poincare’s habit to topologize the dynamics of motion in mathematical problems that lacked analytic solutions. In this way, simple algebraic operations repla
r, Ann. N.Y. Acad. Sci. 929:123- 146. Mixing properties in Human Behavioral Style, Karen A. Selz, U.M.I., Ann Arbor, MI. 1992 Dynamical Systems and Ergodic Theory, M. Pollicott and M. Yuri, London Mathematical Society, 1998. Introduction to the Modern Theory of Dynamical Systems, A. Katok and B. Hasselblatt, C
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