Introduction

2014 ◽  
Keyword(s):  
Twentieth Century ◽  
Number Theory ◽  
Algebraic Geometry ◽  
Dynamical Systems ◽  
Complex Analysis ◽  
Measure Theory ◽  
Classical Mechanics ◽  
Holomorphic Dynamics ◽  
Holomorphic Maps

This introductory chapter is an overview into holomorphic dynamics—one of the earliest branches of dynamical systems which is not part of classical mechanics. Holomorphic dynamics studies iterates of holomorphic maps on complex manifolds. As a prominent field in its own right, holomorphic dynamics was founded early in the twentieth century, but was almost completely forgotten for sixty years, only to be revived in the early 1980s partly due to the efforts of John Milnor. The field of holomorphic dynamics is rich in interactions with many branches of mathematics; such as complex analysis, geometry, topology, number theory, algebraic geometry, combinatorics, and measure theory. This chapter briefly explores the extent of such interplay.

Dynamics of automorphisms of compact complex surfaces

2014 ◽  
Author(s):  
Serge Cantat
Keyword(s):  
Algebraic Geometry ◽  
Dynamical Systems ◽  
Topological Entropy ◽  
Complex Analysis ◽  
General Setting ◽  
Closed Field ◽  
Complex Surfaces ◽  
Algebraically Closed Field ◽  
Compact Complex Surfaces ◽  
Kähler Surfaces

This chapter describes the dynamics of automorphisms of compact complex surfaces when it is rich. In particular, the chapter carries to this general setting the interplay between ideas from ergodic and pluripotential theories. The study is restricted to compact Kähler surfaces. This is justified by the fact that the topological entropy of all automorphisms vanishes on compact complex surfaces which are not Kähler. Moreover, no proof is detailed in this chapter, but a few arguments are sketched in order to enlighten the interplay between algebraic geometry, complex analysis, and dynamical systems. Furthermore, when a result holds for automorphisms of projective surfaces over any algebraically closed field k, the chapter mentions it.

Matrix Completions, Moments, and Sums of Hermitian Squares

2011 ◽  
Author(s):  
Mihály Bakonyi ◽  
Hugo J. Woerdeman
Keyword(s):  
Linear Algebra ◽  
Undergraduate Students ◽  
Complex Analysis ◽  
Measure Theory ◽  
Complex Function ◽  
Complex Function Theory ◽  
Extensive Discussion ◽  
The Subject ◽  
Processing Control ◽  
Developing Area

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.

Introduction

2017 ◽  
Author(s):  
James Whitehead
Keyword(s):  
Twentieth Century ◽  
Literary Criticism ◽  
Cultural History ◽  
Intellectual History ◽  
Historical Sociology ◽  
Cultural Representations ◽  
History Of ◽  
Television Film ◽  
Popular Image

The introductory chapter discusses the popular image of the ‘Romantic mad poet’ in television, film, theatre, fiction, the history of literary criticism, and the intellectual history of the twentieth century and its countercultures, including anti-psychiatry and psychoanalysis. Existing literary-historical work on related topics is assessed, before the introduction goes on to suggest why some problems or difficulties in writing about this subject might be productive for further cultural history. The introduction also considers at length the legacy of Michel Foucault’s Folie et Déraison (1961), and the continued viability of Foucauldian methods and concepts for examining literary-cultural representations of madness after the half-century of critiques and controversies following that book’s publication. Methodological discussion both draws on and critiques the models of historical sociology used by George Becker and Sander L. Gilman to discuss genius, madness, deviance, and stereotype in the nineteenth century. A note on terminology concludes the introduction.

Dynamical Systems in Number Theory

1982 ◽  
pp. 157-177
Author(s):  
I. P. Cornfeld ◽  
S. V. Fomin ◽  
Ya. G. Sinai
Keyword(s):  
Number Theory ◽  
Dynamical Systems

Race, Immigration, and the American Welfare State

2012 ◽  
Author(s):  
Cybelle Fox
Keyword(s):  
Twentieth Century ◽  
Labor Market ◽  
Welfare State ◽  
Political System ◽  
Political Systems ◽  
State Development ◽  
European Immigrants ◽  
Welfare State Development ◽  
Market Relations

This introductory chapter provides an overview of the three worlds of relief created by the intersection of labor, race, and politics in welfare state development. Blacks, Mexicans, and European immigrants inhabited three separate worlds in the first third of the twentieth century, each characterized by its own system of race and labor market relations and its own distinct political system. From these worlds—and each group's place within them—three separate perspectives emerged about each group's propensity to become dependent on relief. The distinct political systems, race and labor market relations, and ideologies about each group's proclivity to use relief, in turn, influenced the scope, reach, and character of the relief systems that emerged across American communities.

Introduction

2016 ◽  
Author(s):  
Leah Platt Boustan
Keyword(s):  
Twentieth Century ◽  
Labor Demand ◽  
Housing Markets ◽  
Black Migration ◽  
The North ◽  
Economic Progress ◽  
Industrial Cities ◽  
Black Economic ◽  
Black Residents

This introductory chapter outlines the central themes and methodologies underpinning this book. It discusses the factors for slow black economic progress in the North following the Great Black Migration. Despite the promise of the North and despite optimistic predictions, black migration to industrial cities did not lead to economic parity with whites either for the migrants themselves or for their children during the mid-twentieth century. This chapter introduces a new element to the story by pointing out that that the persistent influx of black migrants to northern labor and housing markets had created competition for existing black residents in an economic setting already constrained by weakening labor demand and northern racism.

Introduction

2019 ◽  
pp. 1-30
Keyword(s):  
Twentieth Century ◽  
Korean War ◽  
State System ◽  
Nation State ◽  
Territorial Sovereignty ◽  
The Korean War

This introductory chapter provides an overview of the book's main themes. This book tells a story of the changing script of warfare in the mid-twentieth century through the Korean War. At stake in this conflict was not simply the usual question of territorial sovereignty and the nation-state. The heart of the struggles revolved around the question of political recognition, the key relational dynamic that formed the foundation for the post-1945 nation-state system. This book argues that in order to understand how the act of recognition became the essential terrain of war, one must step away from the traditional landscape of warfare—the battlefield—and into the interrogation room.

Introduction

2018 ◽  
pp. 1-11
Author(s):  
Roger Davidson
Keyword(s):  
Twentieth Century ◽  
Sexual Practices ◽  
High Court ◽  
The Social ◽  
Witness Statements

The introductory chapter fulfils three objectives. First, it locates this study within the existing, somewhat disparate, historiography relating to sexuality and sexual practices in twentieth-century Scotland and summarises the aims of the book. Secondly, it explores the strengths and weaknesses of Scottish High Court and Crown Office records as a source for the social historian. In particular, it examines the importance of precognitions − witness statements, including testimony from medicsl experts and the police compiled by the Procurator Fiscal prior to any prosecution. Thirdly, it provides an overview of the structure and contents of the study.

Introduction

2019 ◽  
pp. 1-13
Author(s):  
Christine Kelly
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century

The introductory chapter provides an overview of the main themes discussed in the book and its key insights. It highlights the legacy of reform, commenting on some of the connections between the nineteenth-century history explored in the book and later developments in twentieth- century Scotland, including the links between the earlier history and the seminal Kilbrandon Report in 1964.

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