Overview
- Editors:
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Ryuzo Sato
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The Center for Japan-U.S. Business and Economic Studies, Leonard N. Stern School of Business, New York University, New York, USA
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Rama V. Ramachandran
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The Center for Japan-U.S. Business and Economics, Leonard N. Stern School of Business, New York University, New York, USA
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Table of contents (10 chapters)
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Front Matter
Pages i-xiii
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- Ryuzo Sato, Rama Ramachandran
Pages 1-51
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- Fumitake Mimura, Takayuki Nôno
Pages 107-134
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- Ryuzo Sato, Shigeru Maeda
Pages 135-174
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Back Matter
Pages 301-304
About this book
Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo gists, chemists and philosophers.
Reviews
' This book is recommendable to mathematicians in the field of differential geometry and calculus of variations, who take an interest in economic applications ' Journal of Economic 55:3 1992
Editors and Affiliations
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The Center for Japan-U.S. Business and Economic Studies, Leonard N. Stern School of Business, New York University, New York, USA
Ryuzo Sato
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The Center for Japan-U.S. Business and Economics, Leonard N. Stern School of Business, New York University, New York, USA
Rama V. Ramachandran
