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.