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Dynamical Scale Transform In Tropical Geometry (Hardcover)
Loot Price: R2,047
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Dynamical Scale Transform In Tropical Geometry (Hardcover)
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This book provides comprehensive analysis of dynamical systems in
tropical geometry, which include the author's significant
discoveries and pioneering contributions. Tropical geometry is a
kind of dynamical scale transform which connects real rational
dynamics with piecewise linear one presented by max and plus
algebras. A comparison method is given which estimates orbits
corresponding to different rational dynamics by reduction to the
piecewise linear dynamics.Both rational and piecewise linear
dynamics appear in many important branches of mathematics. Tropical
geometry can play a role or function to bridge between different
subjects in mathematics. This book contains detailed accounts of
basic strategy on how to apply tropical geometry to analysis in
various mathematical subjects by presenting several applications
which include: a rough classification of partial differential
equations from the point of view of global behavior of solutions;
construction of the infinite quasi-recursive rational dynamics,
based on the automaton of the Burnside group by Aleshin-Grigorchuk;
study on nearly periodicity of the pentagram map on the moduli
space of the twisted polygons; spectral coincidence between
lamplighter group in theory of automata groups and Box and ball
systems corresponding to KdV equation in soliton theory.This book
is self-contained, and detailed accounts of theory of automata
groups, BBS and the pentagram map are also included.
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