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Books > Science & Mathematics > Physics > Classical mechanics
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P-adic Deterministic and Random Dynamics (Hardcover, 2004 ed.)
Loot Price: R2,395
Discovery Miles 23 950
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P-adic Deterministic and Random Dynamics (Hardcover, 2004 ed.)
Series: Mathematics and Its Applications, 574
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This is the first monograph in the theory of p-adic (and more
general non-Archimedean) dynamical systems. The theory of such
systems is a new intensively developing discipline on the boundary
between the theory of dynamical systems, theoretical physics,
number theory, algebraic geometry and non-Archimedean analysis.
Investigations on p-adic dynamical systems are motivated by
physical applications (p-adic string theory, p-adic quantum
mechanics and field theory, spin glasses) as well as natural
inclination of mathematicians to generalize any theory as much as
possible (e.g., to consider dynamics not only in the fields of real
and complex numbers, but also in the fields of p-adic numbers). The
main part of the book is devoted to discrete dynamical systems:
cyclic behavior (especially when p goes to infinity), ergodicity,
fuzzy cycles, dynamics in algebraic extensions, conjugate maps, and
small denominators. There are also studied p-adic random dynamical
system, especially Markovian behavior (depending on p). In 1997 one
of the authors proposed to apply p-adic dynamical systems for
modeling of cognitive processes. algebraic structure of fields of
p-adic numbers, but by their tree-like hierarchical structures. In
this book, there is presented a model of probabilistic thinking on
p-adic mental space based on ultrametric diffusion. There are also
studied p-adic neural network and their applications to cognitive
sciences: learning algorithms, memory recalling. Finally, there are
considered wavelets on general ultrametric spaces, developed
corresponding calculus of pseudo-differential operators and
considered cognitive applications. This book will be of interest to
mathematicians working in the theory of dynamical systems, number
theory, algebraic geometry, non-Archimedean analysis as well as
general functional analysis, theory of pseudo-differential
operators; physicists working in string theory, quantum mechanics,
field theory, spin glasses; psychologists and other scientists
working in cognitive sciences and even mathematically oriented
philosophers.
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