Tsuyoshi Kato – författare

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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 theme of this book is to establish a link between gauge theory and L²-cohomology theory. Although both theories focus on differential topology, they have been developed rather independently. One of the main reasons lies in the differing characteristics of these theories. This book introduces an integrated theory that bridges these subjects. One goal of the book is to propose differential-topological conjectures that are covering versions of the so-called 10/8-theorem. We include various pieces of evidence to support them. This book is almost self-contained and is accessible not only to graduate students in differential geometry but also to both the experts in L²-cohomology theory and gauge theory. This unique and fundamental book contains numerous unsolved problems, suggesting future directions of topology of smooth 4-manifolds by using various analytic methods. After the introduction (Chap. 1), Chap. 2 gives a quick overview of the historical progress of differential topology. Chap. 3 covers the basic subjects of spin geometry. Chaps 4 and 5 deal with the foundations of the Seiberg–Witten and the Bauer–Furuta theories. In Chaps 6 and 7, we present the basic theory of L²-cohomology, L²-Betti numbers, amenability, and residual finiteness of discrete groups. In Chap. 8, we treat the Singer conjecture and describe the solution to the conjecture for Kähler hyperbolic manifolds. We then describe various variations of Furuta's 10/8-inequalities and how the aspherical 10/8-inequalities conjecture is induced. We provide the evidence by examining various classes of 4-manifolds, such as aspherical surface bundles and complex surfaces.

The theme of this book is to establish a link between gauge theory and L²-cohomology theory. Although both theories focus on differential topology, they have been developed rather independently. One of the main reasons lies in the differing characteristics of these theories. This book introduces an integrated theory that bridges these subjects. One goal of the book is to propose differential-topological conjectures that are covering versions of the so-called 10/8-theorem. We include various pieces of evidence to support them. This book is almost self-contained and is accessible not only to graduate students in differential geometry but also to both the experts in L²-cohomology theory and gauge theory. This unique and fundamental book contains numerous unsolved problems, suggesting future directions of topology of smooth 4-manifolds by using various analytic methods. After the introduction (Chap. 1), Chap. 2 gives a quick overview of the historical progress of differential topology. Chap. 3 covers the basic subjects of spin geometry. Chaps 4 and 5 deal with the foundations of the Seiberg–Witten and the Bauer–Furuta theories. In Chaps 6 and 7, we present the basic theory of L²-cohomology, L²-Betti numbers, amenability, and residual finiteness of discrete groups. In Chap. 8, we treat the Singer conjecture and describe the solution to the conjecture for Kähler hyperbolic manifolds. We then describe various variations of Furuta's 10/8-inequalities and how the aspherical 10/8-inequalities conjecture is induced. We provide the evidence by examining various classes of 4-manifolds, such as aspherical surface bundles and complex surfaces.

This book focuses on eco-evaluation system monitoring and sensing, carbon-water modeling, mapping, and disaster prediction. It is the 3rd book on tropical peatland issues, following 1st "Tropical Peatland Ecosystem" and 2nd "Tropical Peatland Eco-management" publications. Tropical peatland is also a wetland, mangrove, and rainforest. With this nature, two major key elements of tropical peatland are water and forest. This book introduces the relationship and interaction among water, oxygen, and nutrients as well as aspects of the forest as the driving force of carbon stock and the carbon cycle. Eco-evaluation system is key to conserving, managing, and restoring tropical peatlands, however comprehensive system for Eco-evaluation in the Tropics is not yet established. This book reviews and proposes Eco-evaluation methods in the Tropics Ecosystem, focusing mainly on the peatland ecosystem and others, covering Social Capital such as Credit, Bonds, National Accounting, etc.

This book focuses on eco-evaluation system monitoring and sensing, carbon-water modeling, mapping, and disaster prediction. It is the 3rd book on tropical peatland issues, following 1st "Tropical Peatland Ecosystem" and 2nd "Tropical Peatland Eco-management" publications. Tropical peatland is also a wetland, mangrove, and rainforest. With this nature, two major key elements of tropical peatland are water and forest. This book introduces the relationship and interaction among water, oxygen, and nutrients as well as aspects of the forest as the driving force of carbon stock and the carbon cycle. Eco-evaluation system is key to conserving, managing, and restoring tropical peatlands, however comprehensive system for Eco-evaluation in the Tropics is not yet established. This book reviews and proposes Eco-evaluation methods in the Tropics Ecosystem, focusing mainly on the peatland ecosystem and others, covering Social Capital such as Credit, Bonds, National Accounting, etc.