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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Fully Chaotic Maps and Broken Time Symmetry (Paperback, Softcover reprint of the original 1st ed. 1999)
Loot Price: R2,833
Discovery Miles 28 330
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Fully Chaotic Maps and Broken Time Symmetry (Paperback, Softcover reprint of the original 1st ed. 1999)
Series: Nonlinear Phenomena and Complex Systems, 4
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I am very pleased and privileged to write a short foreword for the
monograph of Dean Driebe: Fully Chaotic Maps and Broken Time
Symmetry. Despite the technical title this book deals with a
problem of fundamental importance. To appreciate its meaning we
have to go back to the tragic struggle that was initiated by the
work of the great theoretical physicist Ludwig Boltzmann in the
second half of the 19th century. Ludwig Boltzmann tried to emulate
in physics what Charles Darwin had done in biology and to formulate
an evolutionary approach in which past and future would play
different roles. Boltzmann's work has lead to innumerable
controversies as the laws of classical mechanics (as well as the
laws of quan tum mechanics) as traditionally formulated imply
symmetry between past and future. As is well known, Albert Einstein
often stated that "Time is an illusion." Indeed, as long as
dynamics is associated with trajectories satisfy ing the equations
of classical mechanics, explaining irreversibility in terms of
trajectories appears, as Henri Poincare concluded, as a logical
error. After a long struggle, Boltzmann acknowledged his defeat and
introduced a probabil ity description in which all microscopic
states are supposed to have the same a priori probability.
Irreversibility would then be due to the imperfection of our
observations associated only with the "macroscopic" state described
by temperature, pressure and other similar parameters.
Irreversibility then appears devoid of any fundamental
significance. However today this position has become untenable."
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