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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.
The Minangkabau, who are from the mountainous region of western
Sumatra, have long been a tangle of paradoxes to the outsider.
Ardent believers in Islam - a partially orientated religion - the
Minangkabau are one of the few remaining matrilineal groups in the
world. A well-educated and enterprising people, they continue to
uphold a seemingly archaic kinship system. They have always been
highly mobile, yet their strong sense of ethnic identity is rooted
in their homeland. Focusing on Minangkabau matriliny and its
relation to migration, Tsuyoshi Kato has written a comprehensive
and authoritative study of the society, history, and traditions of
this complex people. Studies of the Minangkabau since the middle of
the nineteenth century have often indicated that matriliny is
giving way to a bilateral or even patrilineally inclined system.
Kato, however, asserts that the matrilineal system is surviving,
owing to Minangkabau mobility. Exploring matriliny's evolution in
response to changing times, he studies the reasons for the
tradition's resilience. Kato adopts an historical approach,
claiming that a static analysis can capture only part - or
seemingly contradictory parts - of a complex and changing culture.
He examines different types of migration that characterizes three
distinct historical periods: village segmentation - a migration to
establish new settlements - which took place up until the
mid-nineteenth century; circulatory migration to small towns and
markets by individual males, a distinguishing feature of the period
from the late nineteenth century to the 1930s; and the more
permanent Chinese migration, in which nuclear families leave the
village for larger cities, a pattern thatcontinues today. Kato
bases his analysis on his extensive field work in Sumatra and on
such varied evidence as recent census data and Minangkabau proverbs
and legends. Matriliny and Migration, now brought back to life as a
member of Equinox Publishing's Classic Indonesia series, is a
balanced account of change and continuity in a society. It will
appeal to readers interested in Southeast Asia and to sociologists
and anthropologists studying the family, urbanization, mobility,
and the question of ethnic identity. TSUYOSHI KATO received his PhD
degree from Cornell University. He taught at Sophia University,
Tokyo, from 1977-1979, when he joined the faculty of Kyoto
University.
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